There is no 'supercategory', except maybe if you mean something like "game genres that in some way derived from Little Wars".
I mean it in the sense of both Chess and D&D are Games. Chess is a competitive board game. D&D is a tabletop RPG. They're in different categories, but they're both, undeniably, in the Set of Games.
An RPG is different from a storygame, in brief, in that an RPG creates a virtual worlds and players try to immerse themselves in playing characters in that virtual living world; while a story game is meant to tell a story and players take the roles of co-authors trying to craft a story out of a setting and characters that are non-living literary backdrops for the story to happen in and with.
What's an example of a Storygame then? Because I would point to something like Anima Prime as being very heavily storygame driven (players work together to have Group Seeds, to help set the setting, cannot die without their approval as part of driving the plot forward), yet, in actual play, each player assumes the role of a single character. They are to get immersed in just that character.
Similarly, Dogs in the Vineyard seems to have that same sort of flavor. It's all about creating a story (that usually ends with everyone killing each other for being heretics), but during play it's driven entirely by immersing yourself in the character.
A counter example: Exalted. It's undeniably a tabletop RPG, but Stunting explicitly allows a player to break the rules. While in the end it's still subject to Storyteller control, it's still a present factor. Much more so with, say, Fair Folk, where you are assuming the role of one fey whose very job is to create a good story and is actively rewarded or hindered for doing or failing to do that.
D&D, at least as far back as 3E, not sure about further, has had framework and rules for how to do 'shared DMing'. 4E was probably the first one that made it very explicit and 5E still retains that DNA in the DMG.
Honestly, I cannot think of a single game that would fit the description of "characters . . . are non-living literary backdrops" except for, maybe, that spy one brought up earlier in this thread. But even that I'm not willing to definitively state this is a factor in it because I haven't read it thoroughly. Someone better equipped than I can answer that.
So do you have an example of characters as non-living literary backdrops? What games come to mind for you on that? Because under estar's description and categorization I was able to get a pretty good understanding of where he was coming from and what might be considered a wargame v. tabletop game v. storygame to him. I could see fuzzy limits, but limits nonetheless. Here, I still don't see limits, and so the term is empty to me at the moment. It's waiting to be filled with meaning.
If RPGs create anything, it's History.
Not sure what you mean by this. What are you saying is the distinction between history and literature here?
Storygames create a kind of literature. Mostly badly, in my opinion, but some storygamers seem to like that... though I think mostly they like the sense of smugness they get being fans of those games.
I have no basis for comparison on this one, so I can neither agree nor disagree. I have no reason to doubt your experiences on the matter though so... no contradiction from me!