Alexey Pajitnov. He worked for the government, and made Tetris in his spare time across several late nights at his shared workstation. It was a hobby project made out of boredom, not something designed for any ulterior purpose.

He was a fan of those toy puzzle games where you have to fit shaped tiled pieces into a rectangular grid, so he decided to program a version of that for his workstation. When he succeeded with that, he found it rather boring to play with. So he spiced it up by making pieces fall from the top (to add challenge) and made them clear away when you completed rows (so the game would last longer). That's pretty much it. Dead simple. Everything else from the iconic tile colors to the music were added by licensees later down the line.