We should realize the reasons why the Soviet system, the combination of the USSR plus its Warsaw Pact/COMECON "satellites," cannot reasonably be compared to the Chinese situation as directly as most posters here assume. There are two inter-related aspects to consider--the great difference between the Soviet empire and the Chinese one, and the matter of timeframe.
First of all the Soviet system, including the USSR itself, was not, as China was, an ancient unitary empire. The modern Communist regime in China is in many ways a huge break with the Chinese past, but its effective legitimacy (which doesn't address whether I think it's morally A-OK, but the practical issue of how stable it is) rests in a very large degree on continuity with China's Imperial past. An effective majority of Chinese people accept as a premise that China should be a unified state and should control regions that may have local populations who don't agree to this; too bad for them, these places "belong" to China and there are enough core Chinese people committed to the idea that the dissident minorities have no chance to escape--and therefore tend to accommodate to the realities they face.
But while the Bolsheviks did inherit a Russian imperial tradition and did attempt to reconstitute it in a new form, the nature of "Soviet solidarity" was clearly much more contingent on the new regime delivering a radically new, alternate way of life--on it being meaningfully in some sense actually a "worker's state" committed to socialism and the transcendence of capitalism. In the 1960s and '70s, despite the fact that by then many of the trends that would ultimately undermine the system were by then probably irrevocably far along, citizens of the Soviet Union (if not of Eastern European countries) had some material reason to believe that in its own creaky way, their system, which was definitely run on a different basis than Western economies, was in fact getting better at delivering material progress to them. We can see now how and why this was not sustainable and Western ideolouges had been saying so all along, but they weren't allowed to hear Western ideolouges freely and were of course encouraged to point out the flaws and drawbacks of our world and cite the reasons why it was not fair to compare them directly.
For the Soviet Union to reform itself along lines parallel to what worked for the Chinese Communist regime then was much more problematic, because the basic legitimacy of the regime rested on the premise that centralized socialism with a planned economy under Party direction was going to prove to be ultimately superior to Western competitive capitalism, and that supporting it was the most realistic way individual Russians could expect to improve their lives. To turn around and say that actually the Soviet economy should pretty much be run the way Western ones--if not fairly freewheeling ones like the USA, then at any rate more supervised ones like Japan or Sweden--operated, was to say that actually the whole Bolshevik enterprise was a big mistake. When this disturbing message was combined with greater freedom for Soviet citizens to take a closer look at Western realities and compare them with their own lives just recently (when the expansions of access to consumer goods and expanding infrastructure of the 60s and 70s "Brezhnev times" had been stagnating for some time in the 80s) the USSR quite promptly collapsed.
The Chinese could do that because their legitimacy did not rest solely on being Communist revolutionaries; it also rested on their having proven their claim to inherit the title of legitimate government of all China. The Russian-dominated hegemony that was the Soviet system in contrast had much stronger centrifugal tendencies to tear it apart once the premise of a leap forward to a superior social organization under Communist Party guidance was compromised. On paper, the USSR itself was a free federation of diverse nations; toss out Party rule and those nations all went their separate ways. Without the Soviet peoples being committed to the Union, it could hardly dominate the Eastern European satellite states in the accustomed manner; without a genuinely superior economic system, or at any rate one that could offer alternate positive incentives to what association with the West could, there was no chance of persuading these nations to remain allied freely. (Quite aside from a long legacy of bitterness and skepticism about Russians in those formerly captive nations, which would have required some very sweet incentives indeed to placate!)
So all of this indicates why the Soviet Union probably could never have adopted solutions parallel to what worked for China; I wouldn't rule it out completely but on the slim chance that such a long shot could be pulled off, it would probably have been even more crudely repressive on the cultural and political front than even the PRC is today; it is a question of whether sheer terror and intimidation could have substituted for China's ancient cultural capital of the imperial idea to check the many dissidents of the Soviet empire. To be sure if a lightly managed but essentially capitalist Soviet regime did deliver better economic performance in the way the Chinese venture did, more Russians and others too would be attached to the system by their economic prosperity--but the premise of capitalist success is that it is not equally distributed; a new class of "Soviet" businessmen would have a stake in the regime--but the majority of Soviet and COMECON citizens would range from ambivalent (if they were well paid and could buy the more abundant goods) to outraged (the less well paid who might be actually worse off than before and certainly would be losers relatively).
The amount of repression required for success on such terms would probably put paid to any tendency of the regime to liberalize enough to allow anything like the Western Internet, and even the internal network would be even more heavily restricted than the Chinese one of OTL.
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Now on the other hand, I attempted earlier to address the OP in a way that I thought was more realistic--given the perhaps incredible premise that the Soviet system could survive at all. I ask y'all to consider the timeframe issue too. Reforms beginning even as early as 1980 were probably already far too late to save the Soviet regime; to turn it to a more sustainable course on any terms, even Chinese-style "reforms" that amounted to saying Communism is an unattainable mistake, deep change would have had to start happening by the mid-60s or earlier. I proposed instead of reformism that undermines Communist premises, that perhaps if the regime could indeed do as Leftist ideologists in both East and West thought they could and master information technology in a different way than it was being developed in the West then just maybe perhaps they might find new ways to more competently manage centralized economic planning, including the crucial aspect of getting Soviet (and perhaps Warsaw Pact peoples too) citizens to comply. The more effectively the Plans hit their targets, the more intelligently those targets were selected, the better rewarded ordinary Soviet and other Bloc citizens would be for their compliance; thus perhaps the system might move out of the swamp of rampant corruption that mired it down and made a mockery of both economic planning and socialist equality.
Ironically, I felt that the most likely agency to accomplish this miracle of reform on Communist terms would have to be none other than the KGB. It is a question of whether we can believe that perhaps some people from the Communist security police might nevertheless be intelligent and humane, capable of developing a sophisticated system of analysis and control that could manage a growing and flexible planned economy and also help with the police work of identifying and holding accountable those who corrupted the system--and also of the kind of political savvy that let them choose their battles so as to offer carrots as well as sticks and guide the whole society, masses and apparatchiks alike, toward an order that more conformed with the positive ideals of Bolshevism.
Well, the OP says both that the Cold War continues past 1990--therefore the Soviet systems manages to survive in a form the West still sees as threatening--and that there would be some kind of "Internet." I've combined these premises, making the second the basis of the first. But since this alternate Soviet IT would have to be coming on line decades before anyone ever heard of "the Internet" obviously it would have to work on different premises, and making it something that evolves out of security police as first users pretty well underscores how different it would be. It wouldn't be like "the Internet" at all except in the basic sense that in the optimistic scenario, as the technology improves and as the Soviet system, beginning with an improving economic base and moving toward a more secure legitimacy premised more and more on delivery of the socialist promise and positive draws that might even console Eastern European grievances, thus allowing for liberalization across the board and in particular broadening and increasingly trusted citizen access to the IT resources, it would indeed be a network connecting arrays of powerful computers with increasingly comprehensive storage of broad information.
This scenario is actually an inversion then of the modern Chinese situation. In the PRC we have an economic powerhouse on the premise of essentially capitalist competition under Party supervision, where the Party is mainly motivated to enhance Chinese industry's competitiveness and growth--they act essentially as capitalist trustees then, with the added matter of guaranteeing Chinese national security interests to be sure--but since these are construed by men running things largely by and for the industrial entrepreneurs, it's essentially the same in that respect as Western bourgeois nations. Insofar as the Internet today is a vital tool of enterprise, the Chinese regime must permit it, but they scrutinize it carefully, and the society they support does not recognize the liberal values of the West that were also the premises Karl Marx thought to realize in practice. It is in fact quite repressive since it is generally understood that competitive enterprise means massive discontent, and China was ever thus.
Whereas in the rather rosy, early-Strugatskyian vision I've conjured up of a surviving, "Internet"-using USSR with its array of Warsaw Pact allies, the economy and society in general has indeed transformed its base to be nothing like Western competitive capitalism. It is based on central planning for Party-prioritized human needs--including to be sure the need to militarily defend the bloc and so forth. It does not participate in the market economy save to the extent that the regime finds it expedient to sell or buy bloc-produced goods on those markets. It would not be nearly so hungry for Western capital investment as the OTL reality was. Under these circumstances, perhaps despite the long legacy of grudges and mistrust the Bolsheviks added to their Russian inheritance of authoritarian rule, the regime might dare to gradually allow more and more free speech, more and more contact with Westerners, more and more civil rights scrupulously observed--for this too was a promise Marx and Lenin made, that the repressive role of the state would "wither away" under proletarian rule.
So what we'd have would be an economy the likes of Margaret Thatcher or Milton Friedman or other gurus of the gospel of private wealth as the essence of civilization would recoil from in horror as the very antithesis of liberty--and yet increasingly free and widespread use of information technology by increasingly empowered Eastern Bloc citizens.
Call it as crazy and utopian as you like--I think it's more realistic than the Kremlin adopting Deng's policies with a Muscovite accent.