Then surely you believe the GM to not be a player.
I imagine that you're familiar with the very typical contrast, in talking about RPG participant roles, between the
player role and the
GM/referee role. As per my post 18 upthread, replying to you, I hope it's tolerably clear that I am using that terminology.
The moves made by a participant in the
GM role are very different from those made by a participant in the
player role, because they include the presentation of adversity (both in framing situations and in narrating consequences).
A key question, in RPG design and in RPG play, is under what circumstances and in what ways the GM is entitled to unilaterally establish the content of the shared fiction. In fact, I think it's fair to say that this is the cause of more social conflict and of game/group breakdown than anything else in RPGing.
The classic D&D answer to this question is the pre-prepared, and initially hidden-from-the-players, map and key. The reliance on this method is one reason why classic D&D is able to handle only a limited range of situations: because only a limited range of situations is amenable to treatment via the map-and-key technique. Within that range of situations, the only limit on player moves is - as I have posted upthread - what everyone collectively agrees to imagine those characters doing within those situations.
The limitations of map-and-key, in games based around shared imagination, very quickly become obvious. Gygax demonstrates awareness of those limits in his 1979 DMG, in his discussion of how various sorts of dungeon will respond to raids by PCs. The short version is that map-and-key introduces a degree of stability or "status quo" that lacks verisimilitude for many fictional contexts.
It turned out to take a reasonable while - around two decades, roughly from the late 70s to the late 90s - for GM-side methods to emerge that are clear alternatives to map-and-key, but that also put limits on the capacity of the GM to unilaterally establish the content of the shared fiction; though various signs of, or precursors to, those methods can be found earlier (there are hints in 1977 Classic Traveller, more than hints in 1989 Prince Valiant, and then important developments in the 90s with Over the Edge, Maelstrom Storytelling, and probably other RPGs I'm ignorant of).
Obviously, the approach of formally unlimited unilateral GM power over the fiction remains quite popular among RPGers. To an extent that I think many RPGers regard it as an essential feature of this type of game.