What about professional chess? There's nothing in the semantics of the word 'sport' that implies physically exerting. There's a term for that; it's called contact sports.
Well, not really.
Contact Sports is literally sports that have you make contact with an opponent, as a goal of the game or just a side-effect of playing the game.
Soccer and Basketball would be ones where you're not required to touch an opponent, but it happens.
Rugby, American Football, Martial Arts are ones where contact is designed.
A non-contact sport can still be physically exerting, like swimming, athletics, weight-lifting or sailing.
But I agree with you.
There's nothing wrong with a computer game being called a sport, just because it isn't physically demanding.
Chess, Shooting and Darts are all sports that are very lax on physical stress.
And they all require skill to do.
And there's no doubt that to play and succeed in a League of Legends tournament requires skill.