What game would you recommend for someone who hates videogames?

It's never tetris

I could probably write a Tetris clone, but I doubt it would make me any better at playing the game.

I would recommend Okami. It's one of those arty games, has a surprisingly deep and moving story, and it's more about creation than destruction, especially the brush.

Katamari Damacy or something in that vein? It's (mostly) easy, quirky, doesn't take forever to clear a stage, and has a killer soundtrack

If there isn't a game in which game mechanics alone can get you to play, story or no, then there is, frankly, no games out there that you will enjoy. You're better off looking into a new hobby.

As a last resort, you could try Touhou. Most games you mentioned are all sorts of complicated RPG's or other sorts, or 'grand in some other way. Touhou is simple fun, supported by catchy music, in which there is no actual goal besides blowing off steam and getting a high score.

^Problem with Touhou is that it falls squarely into Bullet Hell. And even on easier difficulties it seems like too much frustration for the OP.

@OP: If the very process of playing through a game feels too much like work for you. The I suggest taking a break and doing something else.