The muddling is because there’s an inherent conflict of interest between being both an adjudicator and a player (of the world, opposition, etc). There are traditional ways of addressing it, but I think there’s design space to explore different ones as well. It’s something I’ve touched on a few times here as a motivation for exploring systematic approaches in my homebrew system (often inspired by indie games, hence my comments in
post #91).
I agree that it's a bit too simple to draw the line at "GM is a player" and call that the bright border that defines or guides this as a school of design. I, for example, would contend there's an important difference between the GM playing the opposition, and the GM creating the world and that how one divides those responsibilities between participants has a more significant impact on play than the whole question of adjudication. You can muddle all three of those together (and one could argue that happens most often in the wild), but that's not contingent.
And adjudication isn't particularly clear either; when we discuss the GM as a referee, do we mean they'll be the final authority to resolve unclear rules, or do we mean they'll be designing rules in real time? If they are designing rules, does that authority extend only to places not covered by existing rules, or does it include continuous review of established rules to some other outside metric?
Personally, I think I think what
@clearstream is driving towards may be more about the guiding questions that lead to the design. Those narrative and indie game influences he identifies are not positioned as they are in their source materials; the driving question of the design is not "who has the authority to say what happens next?" That's sidestepped or often explicitly still assigned to the GM, and it isn't boiled down to that question, instead still referencing all those other roles the GM has. You're still playing the opposition, making choices for them that are separate from the PC's actions, and still creating a setting, but additional rules exist to influence what the GM should create, or to limit the opposition's palette of actions.
The question is more "does the GM need unlimited authority over the rules, the setting and the opposition?" and having decided the answer is no, the next question becomes "what is the effect of setting different limitations on that authority?" I don't think it's really worth getting caught up in the mechanism underlying that limitation; quickly you get to the constitution of a game itself and you start having to justify the rules for how a knight moves, which is a separate, not particularly germane discussion.
If you take it as a given that if you tell the GM they must, for example, respect something like a death flag from a player, and can only make choices for the opposition that will result in the player's death when it's indicated, then you end up in a "trad, but" space, which I think is what's being called for, with the design question ultimately being "but what, and why?"