To me the kinds of things that
@Arilyn mentioned that D&D was good at were all kinds of agency. Some examples from Arilyn's post:
1. Agency of discovering plot hooks
2. Agency of Solving mysteries in a traditional fashion
3. Agency of exploring ruins or a strange dark forest that the GM has created
4. Agency of free role play without the need to be guided by dice rolls, which can be disruptive.
5. Agency of having stretches without the constant pressure and busyness of PbtA games
I challenge anyone to tell me why these things shouldn't be described as Player Agency.
#1, #3, and #5. I'm not even sure how to
parse 5 in terms of "agency" at all. You're talking about...a tone? A context? "Pressure and busyness" just doesn't seem to be in any way relevant to the topic of agency. I can only assume I'm missing something from what you're talking about here, since it doesn't seem to have any bearing on "agency" at all.
#1, "discovering plot hooks," is not agency, for the same reason that discovering what lies in the next room of the haunted house ride is not agency. Yes, you are discovering! But you are discovering because the railroad tracks go there, not because you actually made any choices which
produced discovery. Also, see below about how
initiating action is important.
#3, "exploring [locations] that the GM has created," is not agency. It is certainly an
action you can perform. I don't question that in the least! But it is not agency. One of the components of the (philosophical) standard conception of agency is that agency depends on intentionality* and on being
initiated by the agent. This is not,
and cannot be, true of the thing you describe in #3. What initiates the exploration of the ruins or the strange dark forest is
the GM putting it forth, not the players engaging with it. The GM is definitely initiating intentional action, and thus showing agency; the players are not.
*in that
some kind of intentional action must be involved, even if some of the resulting effects are not intentional, e.g. "eating expired food" is an intentional act, but "giving yourself food poisoning" is not, even though both descriptions may be valid for the same act.
#4 is something "supported" (rather, more "not interfered with") by
literally all systems, because the simpler way to describe it is, "Roleplaying without engaging the rules." Which literally anyone can do, at any point, with any system, forever. Indeed, that's literally how at least DW is
supposed to be played. Don't touch the rules, don't do anything
involving the rules, unless and until you meet the trigger for a rule. Then do what the rule says, and when you have your answer about how the fiction should change, return to "free role play" as you put it.
#2 is in a weird position. On the one hand, solving mysteries is an umbrella term that involves a wide variety of actions, and can thus be considered to relate to agency. On the other hand, there is no
specific action to point to in this; "solve a mystery" is not a deed, but rather a catch-all for a lot of related things. So...if we're being technical, "solving mysteries in a traditional fashion" is not, in itself, capable of showing (or not showing!) agency; it is unrelated. If we're being loose, well, it may or may not be related--we would need to get more specific about the actions involved. Consider that the reader of a whodunnit cannot have agency within the story, but can still "solve" the mystery before the detective presents the evidence, assuming the mystery is well-written. No agency, by definition; yet mystery-solving occurs.
Additionally, do Narrative games support all of these types of Player Agency?
Given I flatly disagree that three of the five are even types of agency in the first place, and am on the fence about one of the remainder, no, it does not support them--because it can't support that which isn't even agency to begin with. #4 is literally how DW (and I assume other PbtA games) should be played. #2 is something of a problem, because it can be parsed in one sense as not about agency because "solve a mystery" is not a specific
action one can intentionally perform nor initiate; yet in a different sense, it can be parsed as being an umbrella which contains many actions, and those actions may or may not express agency.