Hayek is an interesting character because "The Road to Serfdom" is not really his finest or clearest viewpoint on markets at all. I saw a video interview with him (you can find it on youtube if you want) where he just restates what I did that the economic calculation problem renders socialism unable to coordinate production effectively.
Russia as compared to the United States is still a backward country. Their wealth is nowhere near the United States and certainly didn't gain any ground during the Cold War period. It doesn't take much, if any, "growth" to force a nation as large as Russia to build a large military-particularly when you don't actually need to figure out the logistics of that army fighting an actual war (since Russia could never have done such a thing against the United States). Add to that forced labor and the basic confiscation of whatever you need to accomplish your goals and it all is pretty straightforward.