You can get single player games.
IMO, if there's no physical effort above that which any other human can achieve then it's a game. Darts, Snooker, Chess...
Sport: an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.
Going by that definition Snooker & Darts aren't sports as they don't test you physically.
Game: an activity that one engages in for amusement or fun...