It’s really gonna depend on what aspect of gaming, if any, she engages with, and figuring that out is a trial and error process that you’re going to have to give her time with on her own terms. Some of the things that are dealbreakers for my Girlfriend are things I wouldn’t have considered because I’m coming to gaming from a 20+ year lexicon while she’s starting relatively fresh from a perspective of wanting to engage with one of my major hobbies.
Mario Kart, Overcooked, and Carcassone (ipad) are the games that my GF and I play together.
Games that have really resonated with her on her phone/ipad, for the satisfaction of puzzling and tactile aspects are Threes, Monument Valleys, Alphabears, Alto’s Odyssey, Doug Dug, Rules!, Card Crawl, the Room series, Scalak, and Gorogoa.
Games that I have recommended her that she bounced off (and in the process I’ve learned she likes smaller loops, more puzzle focused stuff, and self-contained experiences; she satisfies narrative stuff from other media) of are stuff like 80 Days, Rebuild 3 (zombie sim game), The Walking Dead TellTale Games, Breath of the Wild, Mario Odyssey, Samorost (and other point and click adventures), Super Smash Bros, and Snipperclips.
There’s also the non-zero chance that she just won’t really engage with Gaming. It took me a while to realize that, aside from the truly transcendent stuff like The Fifth Season, my GF just doesn’t like Sci Fi, and she’s going to Star Wars with me because she likes me, and I should stop making sci fi recommendations, haha.