I feel the need to point out that you often take this “oh it’s too complex / more complex than your statement” tack - which is really frustrating. If everything is so complex we must write essays with every permutation considered, we can never discuss things. To say that “well we can’t know how much agency a player is given just on the basis of the rules without first unpacking the totality of “system” would suggest we can never really examine agency.
Also, a RPG is a game. It’s in the title

. Once you’ve moved beyond free-form roleplay that functions purely on social consensus and added mechanics, you’re playing a game that can be analyzed using game theory and other tools. Edit: with the simple caveat of “we cannot account for all table cultures.”