The last part here indicate we are not disagreeing at all with regard to the enumeration part? You open for novel interactions, which means you preserve the possibility of actions outside the set actually described by your system. Hence you are not enumerating actions in your system. (Maybe the confusion is in the term enumerate? My understanding of the term is that it involves listing up all possible actions so that you can theoretically give a number to each)
No, I believe the design task is to set a series of rules that can as completely as possible adjudicate any player proposal, using knowable, player facing rules. That most systems fail at this is not an indictment of the goal. Obviously, some abstraction is necessary, but you can get pretty far with a solid range of modifiers and some generic systems, like object hit points and hardness.
I'm not concerned with the precision of those rules as a simulation (though it is obviously helpful and easier to use them if they align with player's intuitions, so that can be a useful design guideline) so much as their predictability and universal application.
But, then how is this system not just as open to your criticism of being "incomplete" due to the requirement for the GM to come in and try to work as a designer modeling a solution based upon existing examples? That exactly the approach taken by basically all traditional RPGs?
The GM as designer of last resort isn't a
good thing, it's a patch to keep the game functioning. The less it occurs the better, and the more a designs celebrates it, the more I can assume it's not going to be a complete game, and the less player agency I can expect. My point was that if it does become necessary, the more complete the system, the less adhoc design work is necessary and the more likely a GM's ruling won't be disruptive to the player experience, because they'll have more existing rules structure to model it on.
And I really cannot understand your second sentence. I guess you are not claiming those playing tournament D&D modules with a scoresheet and defined conditions for getting points were not playing TTRPG?
I'm sorry, I'm also not totally sure what point you're referring to here, though that is an interesting question. I think the ability to support varying and updatable victory conditions is the definitional element of the form. The players agreeing to bind themselves to specific victory conditions ahead of time doesn't really impact that. Compare to a board game; outside of the variance of scenario play, the system of interaction can't be repurposed to broadly support a bunch of goals, and gameplay can almost never continue from the same board state after the evaluation of victory.
Not a point I'd considered before, but your example does make it clear the potential of the rules to be applicable to broad goals and continued play is more significant than the specific goals themselves, or whether play continues.