The Soviet origins of the game were a major selling point of the original Tetris. While the Nintendo version toned it down a bit, it still emphasized the fact that the game was Russian with its American tagline - "From Russia with Fun". At the very least, the marketers of the game in America did not feel that Red Scare backlash would be a problem.
http://americanhistory.si.edu/blog/2014/09/tetris-fun-in-the-cold-war.html
Americans distrusted comunism, not Russia per se. Americans love Vodka and Stolichnaya was imported into the USA by Pepsico, since the ruble was not convertible they traded Pepsi for vodka.
Source: Essentials of International Marketing, Douglas L. Brady
On a side note every Game Boy came bundled with Tetris, hence why the number of sold copies is so high.
The opening screen had Onion Dome buildings and the music is a Russian song. It was pretty obvious it was a Russian game, even to children.