This isn't logical. The game has changed in ways the GM does not have control over by the player leaving. How can you claim that they still have full authority?
Because his authority over the game world and what goes on within it isn't diminished. You the player can leave, but the PC remains or leaves at the DM's decision. Or put another way, if your argument is true, there's nobody ever has full authority over anything.
First, the GM has never had "complete authority over everything that happens within the game"
Nobody in the world ever does by your definition, because all authority is defied by someone.
Second, if a bunch of players fire the GM and a new GM picks up with the existing characters and situation, the first GM still "owns the game"?
The DM literally cannot be fired. Players can quit and find a new DM, but they cannot fire the DM.
In the case you describe above where the players quit and find a new DM, the former DM still owns his game 100%. The players can do nothing about it. He can go and get a new group, keeping the former PCs around as NPCs or not as he sees fit.
The new DM can create a new game with the old PCs, but it won't be the game the players quit. It's entirely new.
Sure, you can take your ball and go home. But unlike Settlers of Catan this doesn't deprive the players of their characters. Can another GM step in? Heck, if you are running a published module can another GM pick up right where you left off?
Not with the same game, no. It will be a new game with a new game starting at the same point in the module, but it's a different game with a different authority figure running it.
"The game" isn't a physical thing like a Settlers set, it's an intangible shared creation. The GM does a bigger share of the set design, the players do a bigger share of moving the story forward.
This is group dependent, not game dependent. Proactive players do as much and sometimes more than the DM to move the story forward, but they still need the DM's backdrop to also move the story forward, and as the DM is reacting to them and controlling more, I'm not 100% convinced that they do more. Reactive players absolutely do not do more.
What does your authority over Settlers allow you to change that?
Nothing. But my authority over the game remains unchanged.
Does your absolute authority over Catan by owning the physical game do anything about that?
I'm not sure what these Red Herrings have to do with the authority. Yes there are things that the DM doesn't control. Those things are all outside of the game.
Please explain how it's both the group effort but only belongs to one person. It's not like we're creating a physical mural somewhere, it's in the shared imagination of the table.
That's easy. The end result was arrived at as a group effort, but the game itself and all of the authority resides with the DM. There's nothing the players can do to change that. Their options are 1) convince the DM to change/compromise things, 2) yield to the DM's authority, or 3) quit and leave the DM's authority behind. At no point do the players ever gain authority of their own unless the DM cedes some to them.
If you start another Settlers of Catan game later with different people, is it still the same game? Or has that first game ("your game" in your parlance) gone away and now you are playing a new game with the same basic configuration.
Yes. It's always the same game. It has the same pieces with the same rules and so on. Game play can differ, but the game doesn't.
If you insist that lighter than air is the only method of flight, you don't need to utter the words "The Wright Brothers will never get their 'aeroplane' to fly", it's implied in what you said.
I never implied it, either. This is wholly a fabrication that you've come up with. Then argued against. That's called a Strawman. Stop it.
When you disputed that the player grants authority and can take it away, and instead insisted that the authority comes from the rules, you are saying that the rules are a higher level of authority than the player. Which means that your premise can only be right if the rules can prevent a player from leaving.
Nope!!! Your logic is faulty. When I said that the game grants the DM complete authority over the game, I am saying and imply ONLY that the DM has full authority over the game. You are trying to twist things so that I'm saying that the game gives authority over the players, which it doesn't and is never the case. The DM has zero authority over the players at any time. At least not from D&D.
Conflating authority over the game with authority over the players isn't doing you any favors.