Mimi: Probably dress-up games like Love Nikki... or life simulator games like the sims 4 etc. He just wants to sit around and make houses or design clothes for hours and do nothing with them
Silver: He gets on Valorant or League or Fortnite with Delta and Lucius every night and they scream at each other for three hours straight and then act like nothing happened the next day. Other than that I don't think he's very picky with games and will generally play anything aside from the fact he does not play horror games ever because he's a wimp. Like not even those spongebob fnaf fangames because he will scream and pass out at the slightest scare
Yura: Stuff like stardew valley and animal crossing! I think she likes being able to relax and do things at her own pace. I think they'd also enjoy games that she can play with friends
Delta: She's a streamer so he plays all sorts of games. Probably also enjoys fashion games because of her personal interest in it but I think he'd also enjoy stuff like final fantasy and nier automata
Lucius: Doesn't really game much outside of the nightly raging game sessions with the bros ngl. Probably the occasional FPS game or something like Doom Eternal (they really wouldn't get why Mimi and yura enjoy games like animal crossing and fashion dreamer and the like)