To me, it seems that you and some other posters are the ones fussing around definitions. I am talking about an actual phenomenon.
When we look at a game, and how it is played - a board game, a card game, a RPG - we can investigate how much control a player of the game has over the way the game unfolds. In snakes and ladders, a player has none. In chess, a skilled player has lots. In bridge, a skilled player has quite a bit, but their control is subject to the hands that they and their partner are dealt.
In a RPG, the unfolding of the game consists in the establishment and development of a shared fiction. In a conventional RPG, the participants occupy asymmetric roles - GM and player - which gives them different moves with which to influence the game. The GM has a special responsibility for setting, framing and (some) consequences; the player has a special responsibility for what one particular character in the fiction does.
We can then investigate how those roles are established, what rules and principles govern them, and from that we can identify how much control the different participant roles have over the way the game unfolds.
I don't know when I first saw the phrase "player agency" used on these boards, but to me it seems to be getting at the idea I've just set out: how much control does a RPG participant, who is in the player rather than the GM role, have over the way the game - which is to say, the shared fiction - unfolds? And that is what I am talking about.
If you want to forbid me from describing that as player agency, OK, whatever - tell me what term I'm allowed to use, and I'll use that. Quibbling over the word doesn't make the phenomenon disappear, or lose its importance to me.
We're just going to have to agree to disagree on this one, I've given my reasons multiple times now. How the agency of the player is expressed varies from game to game, but different does not equate to more or less. It's just different.