This seems to get A Penny for My Thoughts, but that's not a RPG (contra Wikipedia, which I've just discovered classifies it as one). You might try and knock it out based on "shared fiction", but that's not going to be straightforward I don't think.It would appear that the general "you have players and a shared fiction which is developed through interaction of the players" is good stuff and covers those RPGs I can think of, but it also gets other things, so it's not a sufficient definition
So I think your idea of going for core cases and then not fussing too much at the edges makes more sense (it's not like we're administering a RPG taxing statute, so precision isn't essential).
What distinguishes a RPG from a boardgame or boardgame-y wargame? That the fiction matters to resolution.
What distinguishes a RPG from a wargame in which the fiction does matter to resolution? That the non-referee participants engage the fiction, and declare actions, via a particular character who is their mediator/entrance into the shared fiction. Ie those participants, unlike the referee, don't engage the fiction via a "bird's eye view". Or to put it another way, their perspective is not purely authorial.
This also helps distinguish RPGs fro A Penny for My Thoughts. I think the idea that for non-referee participants, their "moves" in a RPG are centrally connected to the characters that they "own" is pretty key. Move away from that and we seem to be heading into "joint story creation" territory rather than "I'm a protagonist in the unfolding story" territory which is characteristic of non-referee participation in RPGing.