The important factor was as the OP says, Malenkov resigned from the secretariat (and as de facto General/First Secretary) in order to retain the premiership, and he'd failed to appreciate that control of the party machinery was much more important that the state bureaucracy. The trouble is though the state bureaucracy was where Malenkov's power base was, he was the archetypal ruthless technocrat - the closest thing to a Soviet Albert Speer - but he wasn't a creature of the party like Khrushchev was. Stalin, Khrushchev and Brezhnev, the three leaders for the overwhelming majority of the USSR's existence were all partycrats, ruthless backroom men who used their influence to take over much of the party apparatus and use that apparatus to further increase their influence and power. Malenkov never really did that, and so failed in his bid for the leadership (the same thing occurred with Kosygin in the 60s).
Had Malenkov risen to the leadership - lets assume he is able to outflank Khrushchev in March 1953 with Molotov becoming Premier and Malenkov General Secretary - the Soviet Union would have gone down a significantly different path. There would have been no explicit de-Stalinisation, much more likely the CPSU would eventually have dealt with Stalin the same way the CPC dealt with Mao's legacy, "70% good, 30% bad" or something along those lines, Stalin's statues remain, his body remains embalmed alongside Lenin's but the terror is eased. Beria is purged and executed and carries the can for Stalin's crimes, Stalin is associated with the five year plans and economic development. Malenkov would certainly have avoided Khrushchev's disastrous Virgin Lands Campaign and Khrushchev's obsession with the development of heavy industry and would have been much more focused on economic development mechanizing agriculture and a rise in living standards. Soviet economic policy would have been led by Malenkov protege's like Saburov and Perkukhin, and would have stuck more to centralized planning than Khrushchev's decentralizing approach, which is likely to present problems. Malenkov is probably dynamic enough to adopt economic reforms earlier though, he's unlikely to follow Brezhnev's approach and quash economic reforms to preserve party unity.
Theres the old quote (i forget who from) that dealing with Khrushchev was like playing draughts whilst dealing with Malenkov was like playing chess, Malenkov was much more complex, much less likely to commit major diplomatic blunders. Malenkov wouldn't have send missiles to Cuba, and he did float the idea of a unified, neutral Germany - something NATO would never have agreed to anyway. The Cold War would be a bit cooler as a consequence, and detente would allow the USA and USSR to reduce their military budgets as in OTL.
If Malenkov is able to remove Khrushchev then his rule is relatively stable. It took year of discontent for the plotters against Khrushchev to finally decide to remove him in OTL, and some of Khrushchev's greatest blunders - the Virgin Lands Campaign, Cuba, radical changes in economic policy - are going to be butterflied away. Malenkov's leadership style is much more stable, and over time he is able to establish himself as a much more powerful leader than OTL Khrushchev or Brezhnev were, no collective leadership. He might even be able to achieve the position of simultaneously serving as Chairman of the Soviet (Head of State), General Secretary (Head of the Party) and Premier (Head of Government), something not even Brezhnev managed to quite pull off in OTL. With steady economic reforms, a stable leadership and a well organised professional bureaucracy the stagnation of the Brezhnev years would be butterflied away, and while the USSR would not have been an economic powerhouse like China it would have been a stable superpower.