In play that is setting-sim, as I have outlined it in the OP, the GM establishes factions, NPCs, and the like with dramatic needs - these are what produce the "living world", as setting-sim is often described. Players make headway in the game by identifying these dramatic needs (eg working out what motivates the various faction, or NPCs) and then engaging with them.
There can be RPGing in which no dramatic need is present at all - @AbdulAlhazred has identified classic dungeon crawling as an example, and I reckon classic hexcrawling could also be an instance of this - but I don't think that sort of RPGing is all that common. I think some degree of drama, even pathos, is pretty popular!
Trophy Dark I've skimmed. Its a game with a strong and fairly simple premise. I think its maybe going to depend on how you play it, and I don't think I'm really qualified to comment much since I haven't, and honestly don't have a complete recollection of all the details of how it frames its process of play.
But, I don't think that narrativist character-driven play requires that the SETTING, the THEMES, or the COLOR need to be defined by or relative to the characters and their dramatic needs. The focus of the trajectory of play, what that talks about, does.
So, another way of defining character-driven vs GM-driven or other forms would be whether or not play challenges and potentially transforms who the character is. And does so at the behest and direction of the player. Classic D&D DC play doesn't do that. Its about an environment, the characters are simply assumed to be greedy adventurers risking their lives for gold. No other sort of motivation is ever contemplated in D&D pre-2e at all. Alignment is just a set of proscriptions. Anything else is mere color. I mean, you can IMPOSE other motivations, sort of, via GM action. Mostly those will be in the form of possible added rewards. Maybe some players will respond to "the town is in danger, you must save it" or somesuch. Pretty thin stuff from a story perspective.
Now, consider BitD, the setting and color are quite well established, as are the themes. The game casts the characters as a crew of scoundrels, but WHY, how they operate, what that means to them, their goals, etc. are all up to them. The system gives you some help, vices, and traumas in particular, plus a rival and enemies/allies you can build off of, but your character's motivations are pretty much your own to author, and the GM is bound to respond to those signals with story elements, which are not prepped ahead.
I don't think I quite understand the distinction here. Isn't greed something that can motivate a character? Why is greed a dramatic need in BitD but not in classic Dnd? Another motivation in classic dnd is exploration, very much in a colonial sense (charting an unknown territory, etc). These aren't very 'elevated' motivations, but are still motivations. Similarly, the crew sheets in blades in the dark tell us a lot about what a crew's goals are and how they go about those goals. Namely, through heists. That's all before the players even write anything on their playbooks and crew sheets.
I think perhaps the difference is in the focalization rather than in dramatic need vs setting. B/X characters have the "dramatic need" of wanting money and power--indeed, the game links the two together in parallel expression (xp for gold)--but the game world doesn't warp itself to always provide opportunities for those...sometimes a room is empty, sometimes there is no secret door. Whereas in Blades, it is assumed that the GM will provide cult-y type opportunities for your cult crew, and not hawker-type opportunities. Moreover, who the pcs know and what they've done in the past will be relevant to future scores.