@Emberashh you (and others) have said many interesting/insightful things, which I may have time and motive to respond to in due course. Here, however, I want to focus on two notions with a view to developing further ideas.
I said
One plays chess in the real world, as it were.
And you responded that...
Stories still happen in the real world, however, so if a story is what one is after, Chess is a possible avenue. The implicit value judgement here is that the stories Chess generates aren't the same as a genre emulating story, and thus they're lesser.
While it is true that the stories are not the same, whether or not one is better than the other is subjective. And moreover, that value judgement also speaks to intention. Baker et al were not exactly coy about pushing genre emulation (ie, storygaming) specifically, and no matter what people may percieve, that is its own game type.
This mistakes the point I am making. No value judgement or even comparison between stories generated by Chess and those from a TTRPG is being made. Rather I am pointing to a categorical distinction between the relationship of play and story. I'm not especially good with examples, but I'll give it a try
Suppose Jo and Addy are playing Chess, and as they make moves each narrates that move. It doesn't bother me how eloquently or elaborately, how realistically or fantastically they narrate. The playing of Chess is the grasping and upholding of its rules, and making legal moves in turn, where given board positions dictate outcomes - such as an end to the game. Their narration is not expected to have any effect on that, nor do the Chess mechanics have the job of driving their narration (compelling and constraining its contents and structure.)
I think you can see that isn't the case with say Blades in the Dark. The mechanics
are about compelling and constraining the contents and structure of the narrative. There are overt linkages between fiction and system. (You can see in a game like Dread the possibility of using Chess as a resolution mechanic in an RPG, but then it would become a tool, like dice, and - as in Dread, or as with dice - there would be rules for translating between system state and fiction.)
Turning then to another notion, I said
At a TTRPG table, players can imagine and continue to imagine things in the yard, so long as they like.
And you responded that...
I think it should be considered that this is just as possible in a video game. The use of a rendered, physical/digital gamespace doesn't preclude the capability to percieve the overall "scene" as something more than its parts.
Continuing to reference Blades in the Dark, one general mechanic is called "progress clocks". These can represent anything in fiction where participants want to "track ongoing effort against an obstacle or the approach of impending trouble." Cases - even within the spooky heist fiction of Duskvol - are limitless. Another detailed mechanic is Vice, which characters use to shed stress. It has linkages to fiction in the consequences of "overindulgence". This mechanic is expected to cause change in the fiction, which the player will go on to narrate according to the constraints of those changes, such as by imagining in accord with the rules for Entanglements.
The designer of BitD, John Harper, drew a diagram of what he expected to see in play, in which the core play loop drives via uniform currencies (rep, turf, heat and coin) which are output from improv play (compelled and constrained by various core mechanics + specifics on player-owned character sheets) progression for the players shared "character" i.e. their crew.
@pemerton I believe this provides an even more satisfactory example for the character sheets - currencies - fiction discussion in your OP. Looking at both character sheet and crew sheet, and their ledgers of very-obviously-currencies that translate fictional positions into system states (and back).
The words "compel" and "constrain" describe very well what Harper's mechanics are doing in relation to the fiction. If it becomes interesting to do so, down the line I think I can connect my thinking here with arguments tackling your notion of aesthetics from MDA.
I would agree that the diagram you linked offers a practical tool for general game design, while adding that it does not answer the distinct problems found in TTRPG. It doesn't address solving those as acutely as Baker's work. As implied in the example of Chess-as-dice above, we have to design something additional to address them. Games are in a family, but they are not identical in every respect - resulting in incompletely-overlapping sets of problems.
As you go on to say
The difference comes in making those additional imagined elements a new and integrated part of the gameworld, which is where the improv game comes in.
Which I think captures quite well some of the non-overlaps, but we must go further, and understand that what those additional elements can be, and the improv game itself, is in TTRPG expected to be compelled and constrained according to shared norms overlaid by adopted rules.