I am not a big fan of First-Person Shooter games, but there are a couple from Valve, Portal and Portal II, which are pretty cool. You have a gun, but it doesn't shoot people; it shoot portals in walls, floors, and ceilings. It is a puzzle game, where you use portals to get around obstacles, such as pools of toxic waste.
There are also a lot of building/harvesting games, like Stardew Valley, Critter Cove, Coral Island, Teddy's Haven.
There are a couple of hotel simulators, and a of couple grocery store simulators.
There are Real-Time Strategy games, where you send out troops to fight enemies. It is displayed as groups of tiny soldiers moving across the map--no actual first-person combat.
Rez, originally for the Playstation II, but now available on Steam as Rez Infinite, is a rail shooter game. You travel along a fixed path while you try to shoot objects that are firing at you. (The plot is that you are a hacker inside a computer, disabling its security mechanisms. What makes Rez cool is the music, which is synchronized with the action, and gets more and more intense as you go deeper into the game.
My wife and I both hate First-Person Shooters, and we still manage to find a bunch of games to play. (On some platforms, my handle is Reluctant Gamer, because I used to feel the same as you about computer games.)