The rise of technical intelligentsia can be seem in the USSR from about the 60's, and yes, much of the culture of that period was centered around that class of people — biologists, engineers, scientists, etc.

There were two reasons of this. First, it was state-approved after a decade of the space race, the Cold War, the general theme of rebuilding after WWII, getting ahead of the West, etc. The second reason was that the literary culture and the arts couldn't compete for a while because most of the major writers either died in the purges, or in the war, or were spending their time in the camps. There were very few people still writing the good stuff, compared to the 'Silver Age' 30 years back. Which created a cultural vacuum of sorts, and it had to be filled.

And so the "physics vs lyrics" debate that was lost by the lyrics — temporarily that is. The technical intelligentsia folks became not only the protagonists of films and books, but they were also some of the main consumers and distributors of the 'unofficial high culture' of the time. Now, by saying unofficial, I do not mean it was anti-communist — quite the opposite, it was very pro-communist, and the absolute majority of the technical intelligentsia was very pro-communist as well — but the unofficiality of it came from it being created and distributed by unofficial sources. Like, songs by the fire kind of things. It was also the rise of the Soviet sci-fi, much of which was questionable, to say the least, when it came to its correlations with the party course. Strugatsky brothers are a good example of that.

You could probably call it the folklore of the post-war period — because even though it was technically only a subculture, it is the culture that the time is remembered by. You could also call it romantic — because they did want to make it have a romantic feel, and that was the major appeal of, what made it so popular at the time. It was also escapist as hell — since none of the technical intelligentsia had any actual institutional power, and whenever there was a conflict on the institutional level, they would always lose — so dressing like Hemingway and going on field trips was their way of being human.

It eventually went downhill with the USSR's subsequent economic difficulties, as engineer salaries dropped and scientific institutes started closing down — and the literary culture has by then also taken another course that quickly overtook the science-focused writing of the 60's and the 70's.

As to how the Rubik's cube was marketed — honestly, it didn't need to be. It was colorful. Very colorful. Colorful things were in favor, and many people just liked carrying it around without the intention of actually solving the puzzle.

And Tetris was not something that the Soviet kids ever got their hands on — it wasn't until after the collapse of the Soviet Union when cheap hand-held games like this were in any way available. And even then, it was only for the lucky ones.