That seems to imply that a player in a dungeon-based campaign has less agency than one in a wilderness or urban campaign. It also seems to imply that a player with a faster character has more agency than one with a slower one.
For the dungeon based game versus wilderness based game, I don't know if that's always applicable. I mean, my games tend to contain both those elements and more....so I don't know if defining them as such at the campaign level is all that useful. But, I tend to think that generally speaking, characters being in a wilderness environment are not as constrained as those in a dungeon, right? I mean....that's the key difference, I would think. You can only move according to the boundaries and properties of the dungeon, which tend to be far more restrictive than ones in the wild. Generally speaking, of course....someone can no doubt come up with some example that runs counter to this.
But I don't know if this dungeon versus wilderness angle is all that meaningful. I mean, the context of each area as established by the fiction and events in the game so far may place far more importance on what happens in the dungeon.....so perhaps the agency found there by the players is far more important and meaningful in how the fiction unfolds. So I think there is more to it than simple geography, although that can be a part of it.
As a basic example, my PCs in my 5E game played through Tomb of Annihilation. In the Tomb, they could eventually face and defeat Acererak, and thereby shape many significant events for the future of the campaign. At any point in the trek through the jungle to get to the Tomb, they could not exercise any actions that had such meaningful implications for the game. Sure, they could use magic to fly 50 feet into the air and they could see for miles in some areas.....but does this mean that the agency they had in the wild is greater than that they had in the dungeon? The players were free to declare more of a variety of actions for their characters, but any such instance did not have as significant an impact on the fiction. Again, there will be exceptions, but I think my point is clear.
As to movement speed, I don't think it's fast/slow that matters. It's the options available. Can the fighter traverse the 200 foot chasm? Can the wizard with teleport memorized? Who has more options to bring about the outcome? If the characters find themselves in over their heads, the fighter's ability to retreat is limited to his movement (barring assistance from others, or the appropriate magic item, etc.). The wizard can run just as fast, most likely, or very close to it, and also has Fly, Spiderclimb, and Teleport memorized.
I think it's very clear that the wizard has more agency in those instances. He simply has more options at his disposal, and those options have different ways that they interact with the fiction.
I would be inclined to disagree (though it's clear I look at agency very differently from you). If the only difference is movement, the players definitely don't have different agency over their characters; they might (depending on game and mechanics and whatnot) have less agency over the larger fiction, because there might be less they can accomplish, but I don't see that as set in stone.
I don't think that the ability to control the actions I declare for my character is really all that meaningful an example of agency unless it is also coupled with some chance that these actions I declare actually can impact the fiction. As others have pointed out, players declaring actions for their characters is present in all RPGs except for perhaps a few fringe exceptions. So we have to go beyond the declaration itself, and look at what that declaration can accomplish in the fiction.
I think that many are looking at player agency as "I am able to declare all actions for my characters, and no one else can do so, barring certain specific instances" and I think that's only a very small part of it. I do think that a player controlling their character, and not being restricted in how they do so is generally a good thing.....I just don't think it constitutes a meaningful definition of player agency for the context of this conversation.
If I am simply able to say "My character tries this" and it happens, then I have agency. If I am able to say "My character tries this" and we use dice to determine success, then I have agency. If I say "My character tries this" and the GM has to determine if it's possible.....here's where it gets tricky. I may still have agency because my desire may come about in the fiction (ME: "I want to kick in the door"--->GM (decides by fiat): "The door goes flying off its hinges"; in this way the GM has facilitated my agency, as
@pemerton mentioned earlier). But if the GM unilaterally decides to block my action, then it's a restriction on my agency (ME: "I want to kick in the door" ---> GM (decides by fiat): "You try your hardest, but the door simply will not budge").
Of those three admittedly basic processes for the game.....1) action simply happens, 2) we use dice to determine outcome, or 3) GM decides yea or nay......only one of them can result in 0% agency. Not that it always does or even mostly does.....but only one of them has it as a possibility.
Would you agree with this?
If so, then a player declaring actions for his character does not display agency in and of itself.....because the GM can deny every single action. Again, this is why we have to go beyond simply the declaration. We have to look at the effect that these declarations have on the fiction.
Can that player shape events meaningfully through the actions that he or she declares?
I think what's happening in this conversation a lot is that people are looking at it as "agency is good" and "My game is not bad" so "My game must have agency". And I think this is leading to some real contortions and justifications to prove that agency is present. I am not saying this is true of you, but I think that it accounts for the fact that there are different definitions of agency being used in the discussion.
If we take away the idea that "agency is always good" and then just start to look at it as a thing that exists or does not.....that there are good instances of agency being removed, and there are bad instances of agency being present.....then we have a clearer view.
In D&D, every choice I make for my character potentially grants agency in some ways, and may cost me agency in others. This can apply to chocie of race, class, background, subclass, spell loadout, feats, and gear, among other things. If I choose to play a fighter, I am willingly accepting stronger limits on my ability to have my character move in ways other than those that are available to all characters. I am accepting that I will not cast spells (barring choice of a subclass that allows it, or multiclassing or similar) nor will I likely have an animal companion and so on.
None of these are bad....because I want to play a fighter. As such, I accept that my character's ability to teleport will be nil.