I do have to say, being challenged like this is forcing me to refine my definitions, which is very useful.
I think I might have a way to cut through this.
All games require some sort of play space. I think we can all agree on that. Whether it's a vaguely defined space like tag (a game played by children generally, so, rigorous attention to rules is perhaps not a priority) or a basketball court or a board or whatever. Games need some sort of space to played in.
Now, here's where RPG's are different. The play space of an RPG is created independently of the RPG itself. And I can prove it. Firstly, most of us have used a module or a setting in different systems. Keep on the Borderlands was mentioned. I've played that in Basic, 1e, 2e, and 3e D&D. Sure, just variations of D&D. But, I've also played it in GURPS and Savage Worlds - two completely, incompatible games. But, you can play Keep on the Borderlands in many different systems with little or no change.
Secondly, I can buy/make system agnostic setting and adventures. There's a truck full of system agnostic settings and adventures out there right now. A quick google search and you can find dozens, if not hundreds of them. Some are limited by genre (fantasy, SF, whatever) and some are even broader.
Now, how would you make a system agnostic board game play space? How would you make a play space that I can play Chess and Catan on? I can't even imagine how you would even start to make a system agnostic play space for games. But, we take it for granted that RPG's have play spaces that are created completely independently from any system.
Which is why I call RPG's game creation engines. They are tools for building a game in conjunction with the play space that is created independently of the system itself. No other games have this ability. You cannot create the play space of a game independently of that game. That's an inherent quality of all games.
Now, once you've wedded your game creation engine to your play space, NOW you have a game. Now you can go forth and play. But, each half on their own is not a game. RPG's can't be played without a play space. You can't play a play space without some sort of mechanical framework that makes it a game. It's the combination of these two elements that makes an RPG a game which is distinct from pretty much any other kind of game.
Doesn't this ignote that, in D&D (and other RPGs) sometimes people just grab the pieces and play?
"Hey let's see how a bunch of 10th level PCs do against a great wyrm red dragon?" - no setting, nothing else.
I've had variations of this from 1e forward.






