Its time for the Journey Gang
Yun: board games, big into jenga and Clue he often lets Karolin win at games but will try extra hard to beat Anre, For video games, he is into Cooking Mama especially when the recipes are accurate to their real-life counterparts, Mistery visual novels or any game with a good engaging story, I also feel like he would be into civilization for some reason.
Anre: Blackjack, old maid, and all sorts of card and luck base games (one of the first scenes of the novel has him and Yun playing poker) wack-a-mole as his weapon of choice is a hammer and on that note, he loves the strength teat form fairgrounds, as for videogames, games where he can beat Yun, smash bros, Mario cart, Mario party, etc.
Parker: he is not the gamer type he rather have a book so I believe games, the only ones I can think of are Spot Hidden Games and Nancy Drew games, I also think trivia pursuit would be another game he would like.
Karolin: rhythm games girly, she is big in dress to impress, and date sims, I don't know why but she is also giving gacha gamer I can see her having spend more than she should on a gacha, I sense fire emblem heroes energy on her