But, "I play the game this way, thus it's an X" isn't really helpful. I'm not sitting at your table. I have no idea what you're doing and it would be very difficult, if not impossible, for you to tell me what you do, other than in very broad strokes. Like Celebrim says above, if I give personalities to my Bloodbowl players, is
Bloodbowl now an RPG? I'd say no. I'd say I've added role playing to a game and that Hussar's Bloodbowl might be an RPG, but, since I'm the only one playing (well, other than the other people at my table) then that definition isn't really helpful.
If I pick up D&D, there is an expectation, written right there in the rules of the game, that I will attempt to create a fictional persona (a character) and play the game through the eyes of that fictional persona. That is right there in the game books. I'm not making that up. I'm not adding anything. Anyone else reading those same books gets the same advice. You don't have to play Hussar's D&D in order to do that.
The purpose of these definitions is never about specific tables. Why would you want to do that? What difference does it make to that table what they are playing? They aren't going to play differently depending on what label you happen to slap on. But, if I talk about Fiasco and call it an RPG, I'm not really telling you what I'm doing. I could probably play it as a more traditional RPG, but, then again, now I'm playing Hussar Fiasco and that doesn't help you either. OTOH, if I label Fiasco a Story Game, that tells you something. That tells you that this isn't really an RPG, and if you want to play an RPG, then Fiasco probably isn't what you should be looking for.
The point of defining genre is to give everyone a common language with which to discuss whatever that genre is. We gain a common acceptance of that genre and I can say, "Hey, I read a really good SF book last night, it's ..." OTOH, if we try to include every single reader's views on what is SF, then someone who says, "Hey, I read a really good SF book last night, it's" simply leads to an endless list of questions to pin down how that person defines SF. You might have that conversation anyway if the book is on the edge between SF and Fantasy, but, by and large, you now have a solid starting point and you can discuss the book without getting bogged down in semantics. At least, that's the hope.
By saying that X is an RPG, and RPG's share these traits, then when someone says, "Hey, this is a great RPG", I can know, with some degree of certainty what they're talking about.
Yes, we should be as inclusive as possible, but, trying to include very subjective perspectives into a definition is virtually impossible. Someone who is acting at the table in a manner that the game does not presume, is something I'm fairly comfortable excluding from the definition of
that game. I do not want to define a table. That's too subjective and idiosyncratic to ever be of any use to anyone other than the people at that table.