Yeah. FFXII: Balthier would probably play a lot of StareFox and FFXII (if possible, he is vain), Vaan would play stuff like modern 3-d galaga-style remakes and F-Zero, and I'm not sure, but Penelo might be in to DDR.
FFX: Tidus and Wakka would be playing a lot of sports, Auron might play Menu-based RPGs. Post-FFX Yuna would probably play stuff like YuGiOh and Duel Masters, just from nostalgia

Auron, between dying and returning to the farplane, might have played save-the-world style RPGs, to feel better about dying before destroying Sin (which is basically what he did, having orchestrated most off the FFX plot)
FVII: Cloud and Tifa would probaly play a lot of fighting games and Vincent would play spooky, gloomy Silent Hill stuff and RE FPSs, Areth would probably play farming sims, Barret would play football but then get sick of ti because I just realized it would be hard to play with a cannon for a hand. Yuffie might play timed puzzle games. Sephiroth... Probably wouldn't play games, might play The Sims and clean dating sims because of his family complex, or Katamari Daimacy so he could destroy things and absorb them into his power.
FFIII: Luneth, don't know. Really depends how you would have played him. Arc would probably stick to puzzle games and simple, "safe" stuff like Tetris. Ingus would play maybe fighting games, maybe some simple RPGs.
KH: Sora would be into fast-paced stuff, racing and real-time fighting games, Riku would probably play some fighting games and, mainly due to Ansem's influence, stuff like Sid Meyer's Civilization and TurboRisk. Mickey would play Mickey's Magical Mirror and probably any other licensed Disney games he could find.