On a meta level, "failure" in an RPG is when the game stops being fun for those involved. "Fun" is highly context-dependent; there is no single definition that will apply to all gaming groups. For instance, most tabletop games are fundamentally cooperative--the game is structured around a mutually-supportive group of PCs that are trying to accomplish the same general goal. Conflict is supposed to happen between the PCs on one side (maybe with some NPC allies) and NPCs on the other; while some amount of in-group tension may exist, PvP is definitely a failure. On the other hand, nearly all LARPs operate on exactly the reverse principle--PvP (often social) is the
primary conflict type, so when it happens, it's not failure. (Failure in LARPs is more commonly the result of rule-breaking and/or biased adjudication.)
Individually, no two individual gamers are going to have
exactly the same definition of fun. A successful game relies on getting a group together that has sufficiently similar definitions, and then running a game that lives within the overlapping space as much as possible.
Problems often arise on the internet (
where people are frequently wrong) when a gamer with a successful career in one type of group meets a gamer from a very different and incompatible group, and at least one of the gamers insist that their own way is "correct" and the other guy is "doing it wrong." Even beyond the arrogance of the message conveyed, it is typical for "explanations" like "you're immature" or "you're incompetent" to follow along as part of the "you're doing it wrong" argument.
So long as everyone in the other guy's group is having fun, who cares? They may not be doing things the way you would, but that's not important--if you aren't part of the relevant gaming group, your definition of fun is not relevant to that group's collective definition of fun.
Now, if one or more people in that group is not having fun, yeah, someone is "doing it wrong." But here it's very important not to let your own preconceptions of "if I was in that group, then..." override. One of three things needs to happen: either the game needs to move into a more fully shared definition of fun, the people not having fun need to leave the game, or there needs to be some sort of payoff that convinces the people not having fun to suck it up and continue anyway. (I think the last option happens more frequently than I'd like, and I think it's inherently socially unstable--causing resentment--in the long run, but people have a LOT of reasons to pick it anyway, most commonly out-of-game friendships.)
Going to dinner with friends, I may have more to say later....
Edit: And I see my comments are immediately relevant while I was typing this up! Who knew.