I thought it was gonna be about the guy who actually made Tetris, but no they cover that in 2 minutes at the beginning and the rest of the movie is about the American copyright lawyer trying to get the rights for Nintendo.
It's literally all about how bad the USSR is and how good corporations like Nintendo are. When the American arrives in Moscow they take his passport down to an evil KGB bunker and the whole movie shifts to being tinted blue and grey.
There's literally a scene where the Russian programmer says to the American "we want to be free, we want your coca cola and Levi's jeans". If it wasn't so boring this would read as satire of American media in the Cold War.
The History of Tetris is a decent (hour-long) overview without the anti-USSR slant. It doesn't cover The Tetris Company's abuse of IP, sitting on it for years collecting royalties from licensees without innovating anything and suing unofficial clones, but what it does cover, all pre-TTC, seems accurate.