I’ve written before that the distinguishing characteristic of a role-playing game is the judge. I was never completely comfortable with that, however, because I think there might games that do not have a judge which I would consider a role-playing game.
I think—more generally—the key difference is that, in a role-playing game, the fiction matters more than the rules. You can’t justify going against the rules in chess based on the realities of ancient warfare. You can’t justify going against the rules in Monopoly based on the realities of the real estate business. The game is the rules; the fiction is merely window dressing.
In a role-playing game, however, a rule can be overruled based on the fantasy being played out. The fiction is the game; the rules—guidelines actually—are merely play aids. Once the rules become paramount, then it ceases to be a role-playing game—in my view—and becomes a conventional game. The typical way to make this work is to appoint a judge, but there could be other ways to do it.
If you say that a game needs rules then I’m happy to concede that role-playing games—by my definition—aren’t truly games at all.