Having extra rules and physical activity seem like the best way to distinguish them.

[ He's never actually put this much thought into what makes a game a sport, and it's not like he can just look it up now, so those two criteria will have to do. ]

I don't mind - and it's not uncommon in games to give one player a handicap to level the playing field, anyway.

[ And while Akechi is egotistical and competitive, he's not 'crush a little girl in a friendly game' levels of egotistical and competitive. ]