My partner and I occasionally play games together, but they pretty much only play word puzzle games on their own. I'm not very good at word games though, and they don't have very good spatial skills, so we frequently find ourselves mismatched. We have a switch and a single decent gaming pc, and a pretty old laptop.
The biggest hit for us has been Baba is You because it is slow paced, and combines words and logic and spatial reasoning. Our biggest problem was that its not actually coop, so we would just alternate who played, which can disengage the other person. My partner also thought its aesthetic is cute.
Our next positive example is probably Snipperclips is also a pretty slow paced puzzler, is mostly spatial skills, but we could play at the same time. They also liked how interactive the avatars are, and particularly snipping my avatar up.
The first miss is overcooked, it was a bit too chaotic, and my partner felt a little lost and uncoordinated. They don't remember it super well, so we might retry this one at some point if they feel more at home playing video games.
The other miss is Mario Kart, which they liked when we played with 4 player, but not just the 2 of us. I'm significantly better at Mario Kart, and they are pretty competitive. If they get more into games they might be willing to put in some time improving, but not so much right now.
Our worst miss was probably Tricky Towers, I'm decently good at regular Tetris, so I can do okay out of the box at physics based Tetris, but there was too much happening to fast for my partner. Combine that with it the competitive aspect and they didn't enjoy this one at all.
The games they most fondly remember from childhood are Dance Dance Revolution and Guitar Hero, though we have downstairs neighbors under part of our apartment and no dance pad or guitars, SSX Tricky, and the Lord of the Rings movie tie in games.
They think they'd enjoy a game that does movement as input like ddr or guitar hero but is maybe less bouncy, and are open to action games, or games with a story, but they should be easier to control and not be too chaotic. Cute aesthetics and cats are a plus.