Nintendo on the Russian market was called 'Dendy'. It was a thing although personal computers were far more popular and local DOS versions did exist since the 1980s. Pelevin's "Prince of Gosplan" is a 1991 short story essentially about a central planning bureau bureaucrat doing nothing short of playing games on his DOS computer. You can look for yourself which ones received a mention.

Domestic games covered domestic themes such as the Perestroika, the conflict over the black sea fleet with the Ukraine, card games not known outside of russia, folk sports, magics and astrology, the dungeons of kremlin and local takes on the eternal 'beating people up'.

Special interests for foreign products naturally also included themes that had particular relevance to Russia, such as the collapse of the Soviet Union, the conquests of Genghis Khan or Eastern European slums.

Τhere have been arcade machines in the USSR as well. You can playtest them here. I cannot gauge how popular they were outside of anecdotic evidence told by the people from that generation and this is not allowed in this subreddit. I do not know of any books adressing video games in particular.

Video games in the Soviet Union were largely restricted to computer games which themselves were built on pirate clone hardware. The economic and social status of technology in the Eastern Bloc largely excluded opportunities and incentives for companies to establish entertainment entities in Soviet territory. This left it to hobbyists to form small businesses making games on their expensive microcomputer investments rather than form larger studios.

That's the general overview, but let's also talk about the exceptions. There was a particular large publisher which was based in Hungary called Novatrade which did contract programming for clients such as Mirrorsoft and Sega (creating the original Echo the Dolphin). this was a unique situation because Hungary was a far communicative country compared to East Germany or Russia itself, so these sorts of agreements could be worked out outside of strict government regulation.

As mentioned by other posters, there was also a market for the so called "Famiclones" specifically the Dendy. During the negotiations for Tetris, the regulatory software organization Elektronorgtechnica tried to get Nintendo to let them build the Famicom in the United States by showing them a Dendy to prove their manufacturing capability, though Nintendo declined this offer through gritted teeth of an overwhelming desire to sue them.

Arcade games definitely existed in the Soviet Union, though on a very tiny and ramshackle scale. The infamous Poly Play was just an example of local games, but several testimonies including Alexey Pajitnov recall seeing games like Pac-Man available to play out in the world. These were obviously not licensed for distribution in the Soviet Union, though could also have been merely grey market instead of pirated as Germany did have a fairly robust arcade game infrastructure.

We can only really point to a few prominent examples which have come to light over the years, as our understanding of a lot of underground Soviet movements is still very obscure. Many formerly Soviet countries have risen to the level of respectable game developers, though this has occurred closer to the cut-off date of this particular forum.

For further reading:

Game Over: How Nintendo Conquered The World by David Sheff. Includes a general history of Tetris along with that anecdote about Nintendo and ELORG mentioned earlier.

Replay: The History of Video Games by Tristan Donovan. Contains what is by far what is the best overall view of Soviet video games in the pre-Tetris days, though it’s still lacking quite a bit.

Playing at the next level : a history of American Sega Games by Ken Horowitz. Briefly describes some of Sega’s development work with Novatrade though not from their perspective.