I'm trying to describe what is necessary for a narrativist game.
My Definition - A narrativist game is structured in such a way as to produce fiction that revolves around certain player defined aspects of their characters chosen at character generation.
Well, this is not really sufficient. Narrativist play is play that is focused on a premise. That premise has, or begets situations with, moral weight. The characters are fit to address this, have passion (it matters to them), something opposes them, and nobody has predecided the direction events will take (at least in regards to the playing out of the conflicts inherent in the premise).
Some kind of definitions or structure around the stance of the PCs is typical, but it is key in this type of play that it does not define the character. That is, the forces unleashed in play will work to do that, not what is written on the sheet at start.
I think this rules out D&D module style play and many other typically D&D playstyles - play revolves around the module where player defined aspects may or may not ever come into play, and even if they do they may do so sporadically such that the fiction produced isn't revolving around those aspects.
This kind of play is typically focused on exploration and achievement of goals set out at the start, with a fixed milieu designed around presenting a predesigned set of situations to the players. As you say, character is essentially color.
The most common specific implementations of this involve
-Success with complication
-Player defined success stakes (constrained by player principles).
-Limited GM authority (only determining what happens on failure or for success with consequence and having principles further restrict what they can say).
I would just say that GMs are unlikely to be more constrained, given we assume each type of play is actually successful. Sure, some ultra Viking Hat GMs might feel different, but those games generally fail.
But those implementations aren't necessary to have a narrativist game, even if they are typical of most games currently defined as Narrativist.
There's 3 ideas I want to explore
1) What other implementations of narrativist can there be?
There's a vast literature on this topic, though I wouldn't expect it to interest you.
2) Is D&D living sandbox a narrativist game?
First, the idea that games (tables, groups playing together) follow a specific agenda, ala 20 years ago Forge GNS is long dead. The question needs to be "can Narrativist play arise within this kind of approach?"
3) What happens in a narrativist style game if players only ever define success stakes for their character's actions as similar to what would be the stakes for an action in a typical D&D game?
I think this one is probably not too hard to answer, but what is the point? Play doesn't function in a Narrativist fashion! Again, there's plenty of literature on this subject.