The Gen I Fighting-types are all martial artists or athletes, but.. what the heck makes Primeape a Fighting-type? Can’t be its temper because hey, Gyarados ain’t a Fighting-type. If anything its temper should make it a Dark-type, along the lines of Tyranitar, Sharpedo, or Hydreigon.
Well, there was no Dark-type in generation I, and to be honest I think that’s probably the main reason Primeape isn’t Dark/Fighting or something (that’s probably what I would do with him). Given that Primeape is humanoid in shape and has no particularly spectacular magical abilities, it makes sense that his fighting style would wind up having some resemblance to martial arts techniques, even though Primeape doesn’t appear to be influenced by an specific martial art like many other Fighting Pokémon are.