You seem to be making some sort of qualitative argument about weapons (bullets, arrows... fishing rods?) vs non-weapons (baseballs), but I'm not seeing what makes archery categorically different from, say, playing darts, or shot-put (in all cases, a sport involving rapidly accelerating a projectile towards a goal of some kind)
No, not about weapons, about effects. Fishing is violent because it harms fish, not because a fishing rod is categorised as a weapon. I don't think archery is categorically different than darts. Shot-put is somewhat different in that nothing need be damaged in performing it but you're right that the launching of the projectile could be seen as violent. The former two meet both definitions of violence whereas the latter meets only one. The thing with a gun is that any use of them involves violence of multiple kinds.
