QUICK ASIDE to address Crimson Longinus.
You've linked a post to the Alexandrian which accepts as foundational building block for subsequent analysis that his Dissociated Mechanics essay is (a) useful and (b) correct. You're not going to get much purchase here with that. The overwhelming number of participants here engaged in an ENORMOUS discussion on it long ago and almost all of them came to the conclusion that it is neither correct nor useful (in fact, its very much the opposite). I can't relitigate the entirety of the argument/thread at this point (it was 1000s and 1000s of posts), but the crux (from my recollection) was that it had enormous holes in evaluating the very nature of Roleplaying games (it would nonsensically cast 4e and Moldvay Basic "board games" - which was really the point of the initial iteration of the essay - and wouldn't recognize Pawn Stance play as TTRPGing) and it misunderstood certain aspects/deployments of authority distribution as being inexorably caught in the event horizon of "story advocacy"...therefore incapable of being "protagonism" (aggressively advocating for the dramatic need of a constituent part, a Character, of "the <possible> story") rather than recognizing the possible state of independence of the two (while, yes, acknowledging the likely interdependence) despite a given configuration of distributed authority.
Its initial iteration was an extremely controversial partisan hit-piece by someone who didn't understand games they clearly weren't familiar with/didn't like/took offense at, which I think was cleaned up later. Regardless, it certainly wasn't convincing then as a piece of independent analysis and therefore any work that depends upon it as a foundational piece will be compromised.
Cue Forest Gump (That is all I have to say about that).
I'm going to try to do some further explanation here which I hope will clarify how I'm intending to use each of these concepts in developing this matrix.
As a reminder (and Frogreaver addresses this in his 2nd paragraph above), I'm still unsure if there is sufficient utility and independence in separating Character (as a unique object within the gamestate separate from all of the other objects - which would be Setting) from Setting when it comes to (a) formulating a matrix to discuss agency when analyzing play and (b) formulating a matrix to derive agency when conceiving > executing the intentful design of a TTRPG. More on this below.
First...
THINK OF CHARACTER, SITUATION, AND SETTING AS GAME PIECES
Lets start here. This is ultimately what I was trying to get at with "vector" (or medium). Protagonism, Tactical, and Strategic are not game pieces. They are what manifests through the game pieces.
Yes, Situation will have dimensional parameters (the independence and interdependence of Goal/Intent < > Stakes) that can't be plotted as x, y, z coordinates. But for the sake of this effort, leverage those big brains of yours (everyone) to either (a) ignore that or (b) conceive of the possibility of plotting it if you must.
So...
* A Character is a Game Piece (through which a table participant will express/channel Protagonism-based, Tactical-based, Strategic-based agency).
* Any given Situation is a Game Piece (" above).
* The Setting is a Game Piece (" above).
This is where its going to get a little meta.
If we had sufficient vantage and could instantiate any game into infinity, we would see Character and Setting being in a state of Superposition, encapsulating every_single_concievable configuration of their collision (which would be a manifestation of initiating/inciting Situations and all possible downstream Situations similarly in a state of Superposition).
Take any one of those instantiations. Those are your 3 Game Pieces.
There will be ample interdependence between the 3 Game Pieces but is there sufficient independence between each 3 such that it is useful (or even required) to make them discrete when developing a matrix for analyzing play and designing games. I'm inclined to say "yes" but I could be talked out of it with sufficiently persuasive argument.
So...to Character as Game Piece. Again, immersion or habitation need to be set aside here for this analysis. "The sensory and (de)moralizing experience of remembering" and "the sensory and (de)moralizing experience of recognizing relations and having relationships" is relevant to the holistic experience of play. But we have to excise that to honestly engage in this analysis.
So I have this Character. They're here, now, in this space along with other objects (Setting). Now there is a problem where I want something (through my Character) but the relationship of objects (including my Character) in this space conspires to deny me it (my ability to make this what play is about is Protagonist Agency...my ability to advocate for that desire will manifest in Tactical or Strategic Agency). This is Situation.
I do agree that on the Venn Diagram of those 3 Game Pieces ("vectors" or the medium through which a participant at the table will give rise to their Protagonism, Tactical, or Strategic agency), there will be some "conceptual bleed" and overlap (I mentioned a few upthread, but the Mark aspect of a 4e Fighter's Combat Challenge has some meaningful differences from the Immediate Interrupt aspect of their OA which has meaningful differences from the initial, and best imo, iteration of Come and Get It). There is interdependence (but there are discrete things as well).
Lets contrast "Read a Sitch (or Discern Realities in DW)" in AW from a Passive Perception check in 5e.
My initial orientation here is through the Character Game Piece. I'm here and now in relation to all of these objects in this space and I'm in a situation.
I roll dice.
Any result of 7+ and my Game Piece is now either/or/both Situation or Setting (because of the structure of the move, the agenda of play, and the ethos that binds/informs GMing). Through this I'm expressing one or more of Protagonism, Tactical, Strategic agency by generating/directing/focusing content (and/or ensuring other content doesn't manifest).
On a 6-, I'm actually still expressing some agency through Situation or Setting...but it can_only_be_Protagonism Agency; I can, at least in part, dictate that play further interacts with the resolution my PC's dramatic need (because the prospects for erecting a move-based gambit have been wrested from me due to the fortune results and action resolution procedures).
My habitation or sensory experience can (and for those, like myself, who love AW) be entirely unchanged. But what is happening at the game vantage level is what it is.
Contrast with a 5e GM saying "what is your Passive Perception/Insight (?)" when you've unknowingly entered a provocative place or encountered a potentially volatile NPC and giving you an information dump.
Contrast with a 5e player saying "I go to the balcony and look to the northern night sky where the arresting BOOM came from" and the GM saying "Roll Perception."
EDIT - This may look superficially like The Forge's Pawn, Actor, and Director Stance makeup. But, unlike that essay, I'm not attributing a cognitive relationship. Its literally a question of "when looking down at the Game Board, which Game Piece do you pick up to do this thing?" There is fundamentally no need for a cognitive shift (eg from Actor to Director) when "Reading a Sitch" in AW above vs what happens in 5e. You can inhabit both Actor and Director simultaneously, one or the other, or neither (Pawn). Some players may claim that they are incapable of habitation/immersion with one or the other (and others may claim amplification of habitation/immersion)...but that is entirely beside the point to "which Game Piece do you pick up to do this thing?"