Just a brief response: the indie RPG community thinks that it is distinguishing the non-story-telling game of Monopoly from the story-telling game of RPGing (which you are labelling "improvisational acting") not in terms of activity performed (which, as you note, might sometime be indistinguishable) but in terms of purpose for which that activity is performed. That is, GNS distinguishes playstyles not on the basis of activity performed, but the metagame priority that drives that activity.
Now maybe this claim about metagame priorities is wrong (although I personally am sympathetic to it). But it does explain why the indie RPG types think they have an answer to your attempt at reductio via Monopoly as played by the blind.
Again, role-playing and improv acting are different in the same way as asking "is this you or is this you acting?" This distinguishes between fundamentally different ways of being. Trying to equate all behavior with theatre acting may be what is confusing those gamers wanting to play theatre improv games instead of RPGs.
To clarify a distinction you made: I am not saying all RPGs are improv acting games. I am saying RPGs are games with role-playing in them. One can improvisationally act or not while playing them just as one can in any game. To do so does not make those games "acting" games (much less RPGs). See my baseball explanation above.
Now, are you saying that when someone does NOT improvisationally act in an RPG (portray their character's personality) it is NOT a story-telling game? In other words, RPGs are telling a story when done "in-character', but not "out-of-character"? This is a confusion I can understand as the in-character portrayal of a PC displays their personality. That portrayal of personality would count as a story for me just as it would for anyone who watches acting on stage, TV, film, or other format. But as I just said in the previous paragraph, that kind of improv acting can be added to any game. If that's what it takes to be included as a storytelling game, you can relax. The only rule you'll ever need to add to a game is, "Pretend you're another person while playing this game". That rule is totally unnecessary to role-play.
Here's the big difference: Just as in the Mickey Mantle example for baseball, one does not
need to portray a personality to play a role in a game. Baseball, and role-playing, work just fine without anyone pretending to be someone else. In Baseball, you take on the role of a baseballer. In an RPG, you take on the role of, say, a human fighter in a modeled reality. Both the baseball field and the modeled reality are real. If baseball were a game like Monopoly or another boardgame and modeled a fictional idea beyond just the rules, then we'd see things like bases called "stars, moons, planets" in other words, the components of whatever fictional reality we thought it modeled. Typically, the fiction determines the design of these games just as it does when you add house rules to the design of an RPG. The fiction isn't the "real" part, it's just the terminology one enjoys when playing - just as "hotel", "house", and "Jail" are terms referring to models of those fictional things in Monopoly.
If all we were doing was telling a story, all of this would be unnecessary. You would not need to test the player's ability to do the role. [To bring everything back on topic] You could "just say" that Mickey hit a homerun and we could move on with his actor's portrayal.
EDIT: In regards to meta-game priority making games storytelling games. Perhaps my distinction between acting and role-playing (one you seem to refuse to see) is not swaying you for why RPGs are not storytelling. From your explanation, it would seem any "intent" by the participant to tell a story, regardless of what the action may be, is what determines the "telling of a story". To expand, I take you to mean here that theatre acting has nothing to do with making something a story. You could not theatre act and yet have "intent" while doing an "non-theatre action". And simply by having that intent the doing becomes the telling of a story. That you can simply "live" in such a way as to tell a story vs. "living not to tell a story" acting be damned.
This must be the the reason I keep hearing this Black Hole argument of "You can tell a story about it, so it's a story game". But then, of course, you get crazy arguments like Monopoly
not being a story game. Your "meta-game intent" priority rationale disqualifies any such thing as soon as I "meta-gamingly intend" to play Monopoly to tell a story. Then it all counts. Even when I say, "none of our group's RPG games are done with the 'intent" to storytell." I am correct here, as we don't have that "meta-game intent".
This is a myth in my book. Intent isn't a definer beyond normal acting and theatre acting. To agree so means anything could be done without such intent and need to be re-termed for it. The realities of all such "intent" termed actions/games would need to be re-addressed, so as not to confuse anyone coming in without such intent. As I've shown above with "acting during a game" and "not acting during a game" this "Acting Intent" definer seems to have no bearing on titling normal activities.