Depends. If the GM is rolling wandering monster checks out in the open, rolling on the encounter tables and rolling for the number of monsters appearing, plainly out where everyone can see, are the monsters really appearing "by the GM's will" in any meaningful sense? When the GM makes a reaction roll or a morale check for the monsters, can it really be said that the GM will "comprise all possible thought and decision" for the monsters? I very much doubt it.
The GM, I had thought, always has the
choice as to whether they use these things or not. They don't just blindly invoke them like a computer would. If a reaction roll doesn't make sense despite the rules calling for them, the GM can negate that. And, likewise, if a situation arises where the GM feels a reaction roll
should happen even though the rules don't officially call for one, she can enforce that. I don't feel any differently about random monster rolls, and none of that would say much of anything about either the fact that the monsters
literally can't exist or act without the GM's direct participation--as is the case with all parts of the world that aren't the PCs.
Unless you mean to say that old-school rules somehow
prevent the GM from using them as they see fit? That would certainly be a surprising reversal compared to the statements made pretty much everywhere else by everyone else that favors such things.
And if the GM has set themselves up not as "the opposition" to the players but as merely a referee for the game's rules and a maintainer of the fantasy milieu (the one "running the simulation," to use a very crude analogy that I don't like at all), it makes no sense whatsoever to compare the GM being neutral between PCs and NPCs/monsters to the GM being neutral between "themselves and the players." The GM is not the NPCs/monsters, and they are not merely some "aspect" or "avatar" of the GM.
First: If you don't like the analogy at all, why use it? It would seem very much to mean several things you
don't want it to mean.
More importantly, I don't see how "it makes no sense whatsoever." Everything that is run by the GM--meaning,
everything, more or less, except the PCs--exists by and for the GM's interests. They cannot be neutral with regard to things that their
active and continuous assent and participation are required for. They are, very simply,
involved.
That doesn't make them the opposition
personally. I would say exactly the same thing regarding a game where the GM never participated directly in combat at all--where all opposition were different groups of player characters fighting one another. The GM is still
involved because the world--terrain, visibility, supply lines, weather, and adjudication of both edge cases and unexpected deviations from standard procedures--
needs the GM's constant, active involvement, and these things directly impact both sides. They aren't
staying out of the conflict; they're
facilitating it, ensuring that it works out in a way preferable to them (namely, one fun for everyone involved). Even your example GM is nowhere near as "neutral" a party as an arbitrator or judge, and certainly not anything like a country trying to avoid participation in a war.
"Neutral" means non-participation: literally,
not taking part. That's literally part of the definition of the word. "Unbiased" means you don't treat any participant with favoritism.
