Avid LoL scene follower checking in, most players are in fairly good shape. With the scene getting more serious and professional most teams are getting coaches that mandate healthy diets and exercise as part of a team's training, since you know healthy body healthy mind. So while the game might not be that physically intensive (though it definitely can be really stressful) most players do at least undergo some kind of physical 'training'.
Obviously differs from team to team and there are some overweight pros as well.
Obviously differs from team to team and there are some overweight pros as well.