I voted YES.
I think part of the reason many vote no is due to the semantics, or the english use of a word "Athlete". I am not a native English speaker, and we usually use the word "Sportsman", which actually fits better.
I do agree that "athlete" symbolizes someone's physique, and it's tough to wrap your mind around an idea of gamers of all shapes and sizes as athletic. But they most certainly fit the description of "sportsmen" the same as bowling, chess, bridge, darts or snooker. And the main reason many like to dismiss esports is because gaming is still being considered infantile, while darts or pool are adult "sports", mainly because their primary venue are bars and pubs.