My take on the emperors as gamers:
Demetrios: normally 'too cool' to be seen playing games, but not above playing sportsgames like Fifa or PES or beat-em-ups with friends.
Nikolaios: Snobbish gamer, will rave on and on about some 'forgotten jewel' nobody else ever heard about.
Manuel: If he plays a game, he plays to win. Not above cheating/jusing gamey tactics. Enjoys humiliating his opponent. Not sure what his favorite genre would be.
Basil: Would enjoy a good RTS. Would be king of Total War series.
Thomas I: Probably plays beat-em-ups. Would probably accuse opponent of cheating is he loses.
Thomas II: Games like World of Warcraft are invented for him. Would have multiple accounts.