How exactly do you define "game-changing" here? Indeed, there are some natural resources in these areas--though I am unsure if this was known about back in the 1930s and 1940s:
As in: a resource which is extremely valuable and/or sorely lacking in Russia itself; something that could significantly affect its global status; something that's worth inventing an ideological justification from scratch and risking such a massive conflict.
http://www.lib.utexas.edu/maps/middle_east_and_asia/iran_industry_mining78.jpgAlso, for what it's worth, it appears that Bukhara controlled the Uzbek-majority parts of Afghanistan up to the 19th century:
https://en.wikipedia.org/wiki/Afghan_Turkestan
"At the beginning of the 19th century they belonged to Bukhara; but under the emir Dost Mahommed the Afghans recovered Balkh and Tashkurgan in 1850, Akcha and the four western khanates in 1855, and Kunduz in 1859. The sovereignty over Andkhui, Shibarghan, Saripul, and Maimana was in dispute between Bukhara and Kabul until settled by the Anglo-Russian agreement of 1873 in favour of the Afghan claim."
In turn, this could form the basis for a Russian claim to these areas.
However, as I have previously said, Russia might want Afghanistan as an ally in a future war against the British and thus might not aggressively pursue these territorial claims.
OK. Also, though, what about going for all of Iran for the natural resources (oil, et cetera) and living space there?:
http://www.lib.utexas.edu/maps/middle_east_and_asia/iran_industry_mining78.jpg
Well, I suppose Kornilov's origin suggests he could develop some kind of pan-Asian tendencies. So there's one way he'd fit into the scenario, though there's still not much to suggest he'd be a radically expansionist dictator - or even any kind of dictator, necessarily.
Living space? Eh, I still think there's plenty in Siberia and the Far East, or in Central Asia for that matter...and much of Iran is a desert, isn't it?
After all, if Hitler managed to sell a war for Lebensraum to the German people in our TL, why can't a non-Bolshevik Russian leader do the same in this TL? Indeed, I can imagine a narrative of how it is Russia's destiny to expand not only to the Pacific Ocean and into Central Asia, but also to the Indian Ocean!
Not sure to what extent Hitler was really selling a "war for Lebensraum". Lebensraum was certainly no secret, but I imagine the public view - and Nazi propaganda towards the general public - was more keen to emphasize WW2 as the "war to overturn Versailles", "war against the Communist menace", and so on.
Also, @Halagaz, what do you think that Russia's chances would be in a 1940s war with the British Empire over Iran in this TL?
I think Russia would make considerable gains in Iran (and maybe elsewhere); and then, eventually, get overextended, bogged down, and start losing. The final settlement might not necessarily be devastating for Russia - indeed, it could even get a slight increase in territory or influence - but it would ultimately be far less than they originally wanted. Basically, I imagine the war would be something between a draw and a British/coalition victory.