Part of the answer is that what a game is, is constituted between the players and the game.
Hence I employ a philosophical skepticism about knowing what TTRPG is played without knowing both players and game. Players must first interpret the rules, meaning they have a part in deciding what the rules are. Then they must decide how they will use the rules. This is most obvious when there are parts of a game left unexplored by some groups, due to their prioritisation of other parts.
That doesn't rule out designing and choosing designs that are better fit to your purpose, but it does reject the idea that the game has a single identity across all groups of players. That being so, one group can find play in a game that another group doesn't see or accept.
I'm not really disagreeing with you here, just adding some nuance. The question you ask is a live one.