But by your logic, Law and Buggy SHOULD be rivals since they're both pirates after One Piece /:::Once again since you seemed to miss it the first time. No not every pirate is a rival to each other if they aren't pursuing the same goal or pursuing a victory over each other. For any pirate going after OP any pirate content on staying in GL is not a rival. So you can keep throwing around "every pirate is each other's rival" like it's a valid point trying to marginalize the definition of the word but you're the only one actually saying that. And it wouldn't really be every pirate either it'd be every pirate captain. So go ahead and continue trying to downplay it by being hyperbolic.
You also misread my post, I said Law is a rival to Luffy and so is Buggy but Law is a closer rival than Buggy is. Law is a rival in piracy searching for OP and Buggy is a personal rival searching for victory over Luffy. Both are Luffy's rivals. You can have friendly rivalries too so don't bother coming with that an ally can't be a rival. Since Buggy doesn't seem to really be after OP(seems content having his piece of the pie plus he's looking for that treasure Luffy gave him the bracelet to find) then he and Law aren't really rivals
I'd also like to point out by what definition is it narrow to include more people? You actually just called being more inclusive narrow minded. Bravo.
Funnily enough, you ignore one thing in your sports examples. Repetition. Consistency. By your definition, every professional sports team are actually rivals with each other because they're all competing to win the big finale of their season and have similar skill.
Yet, in those examples, that's not the case. In your examples, a rivalry is an exclusive relationship. The keyword being relationship. The teams you listed as rivals aren't rivals with each other simply for existing in tandem with each other while pursuing the same goal, but because they have an ACTUAL RELATIONSHIP of conflict that is more personal than the ones they have with any other given team or person.
Even in those one-sided rivalries, they are on the same level of ability. You need to retain a certain level of exclusive ability to remain, for example, on a football team. And while some teams are way better than the other, they're still in that same ballpark.
Moriah and Kaido don't have this relationship of conflict. Moriah might have a grudge against Kaido because of what he did, but we have never seen the relationship of conflict between being personal and consistent enough for it to be considered rivalry, and not just competition.
Your definition is narrowminded BECAUSE of how inclusive it is. Your outlook on what a rivalry is is so vague and simple, that it applies to an entire population of people. The more simple and dumbed down the definition of something is, aka the more simply and narrowly you look at it, the more people will fit that definition. Your definition of a rival is simply too vague and too broad for the word to have any meaning.