It’s a culture shift and not one I am fond of.This conversation has always been more about usage (prescriptivism) than descriptivism, which is why it has been incredibly disheartening to see people retreat into catcalls about "semantics" and "word games."
I feel like I have to keep quoting the last sentence of the OP:
Again, there are other TTRPGs that are built in a different way, but when it comes to D&D, there is a distinction between players and the DM that is useful to maintain, both as a matter of language and in terms of the roles that they play at the table.
This is why, when you are a DM, you would never say to another gamer that you are a "player," because that term has a specified use in the context of D&D; just like if you were in a group of people that had PhDs in mathematics, you would not say you were a mathematician because you happened to split the check (unless you were either joking or had slept at a Holiday Inn Express). For that matter, the long-repeated, but true, joke is that no matter what your opinion is on PhDs, if someone drops on the ground and someone screams, "Is there a doctor in the house," you probably won't rush forward because you have a PhD in Comparative Literature.
So when people say (as in the quote that gave rise to the OP) that the DM is a player like any other player, then they are not making a descriptive claim about dictionary definitions. This is a normative claim about what D&D is, or ought to be. As you can see, people saying, "Well, maybe that is how it was, but not how it is." And using the idea that this is semantics (and ignoring the context-shift) as a cover for the normative argument about how they want the game to be played. a/k/a, this is how the game should be played, because this is how the term is defined.
Eh, forget it it Jack. It's Chinatown.
people are worried about authority and others cramping their style and identity. That’s not just how it is or how it should be—-for some it’s the focus. Gotta root out bad stuff, it’s everywhere!
can’t have anyone with “authority,” authority is bad. It’s gotta be a drum circle of storytelling.
that is what is driving the resistance to old institutions. Gotta tear down the old.
in practice? We get together with friends. Someone designed a world and adventure. We play in that creation and alter it when we play. The dm roots for us but sets limits so it’s fun and risky. Otherwise it’s just “pew! Pew!” I killed the bad guys ‘cause story!
the culture is shifting. There is some innovation there is some good stuff and then there is ponderous fit throwing whining and resistance.
play with like minded players (as concerns game philosophy). Diversity of opinion is fine to a point unless the opinion is that the game needs to be dismantled. In that case, you can go play in that corner and we can go play in this one.
for some it’s an argument about simple preferences. For others it’s a mindset that is pretty generalized.
I guess for some it’s just fun to argue too