The Soviets dominated at chess for decades, presumably because it was (is?) effectively a state-sponsored sport there, with kids as young as preschool learning the game.
If the Soviets’ goal was to prove their intellectual superiority over the West, they kind of failed. Bobby Fischer aside, the collective attitude of Americans towards chess at the time was a giant shrug. It would be like a Michelin-star chef dunking on some guy’s sno-cone stand. Sure, the Soviets whooped everyone’s ass at chess, but apart from Fischer, no one else was really trying to beat them.
Russia has a long love affair with chess that predates the Soviet revolution by centuries. After the revolution, Lenin, an intellectual, promoted the game and subsidized it as a relatively cheap and productive past time for everyone.
It’s just popular there; I don’t think it’s any more complicated than that.
The USSR pumped effort into developing chess talent just because that’s what they do - look at how they pumped effort into winning Olympic medals - but of course they were going to emphasize pursuits that were already popular, and chess was wildly popular in Russia long before Karl Marx was born. Russians are good at chess for the same reason Canadians are good at hockey and Indians are good at cricket.
Just as a trivia asides,
I didn’t know this until a few years ago, bur Russians don’t have all the same terms for the chess pieces as we do; they call the bishops elephants, for example. I’d presume that is likely closer to the original word for the piece.
As old as chess is, the modern ruleset is a bit more recent than you might assume; pawn promotion to any piece, for instance, is a 19th century idea.
I am not suggesting that either one caused the other. Just that they may reflect the same mentality. Both involve very complex situations with many moving pieces.
We do also call the rook a castle so I guess that makes sense. “Runner” is a cool name for the bishop though. It seems so fitting.
In Russian the queen is called a “ferz,” which I believe is not a Russian word but is borrowed from Persian or maybe India, and roughly means something like “minister” or “vizier” (well, I guess to a Russian it just means "the really powerful chess piece that sits next to the king.) The Russian word for queen is “koroleva” (or “tsarina” if being specific to Russian monarchs) but isn’t used in the sense of the chess piece.
If I may chime in, when I hear Bauer for pawn I think peón (Spanish, where you see the close relation to pawn). Peón has several meanings, one of them being day laborer. Bauer (or Knecht) can mean that as well, and also the lowest rank a soldier can have, like soldado raso o soldado cabo peón (there is the peón again), which is translated into English as private (and here the pawn is lost in translation).
In German, the game is called Schach and “checkmate” is schachmatt. Maybe there was a transfer over German to English, but anyway I think both expressions come from Persia.