One particular point of tensions between drama & aesthetics versus gaming is that the gaming side of things is very often approached from the competitive angle, or more broadly some kind of success/failure perspective, often (though by no means exclusively) with regard to particular tasks. Even RPGs that work with confict resolution are often treated this way, to the point of using "success/fail" terminology. In good drama, the protagonist typically doesn't get what they want right away, on several timescales, but this isn't necessarily presented as failure—that depends on the themes & ideas the author is going for, of course. There's a trick to authoring good fiction that keeps such things interesting rather than discouraging, which is easier for a reader who can assume the story is going somewhere, due to artistic conventions. To put that into any kind of system for generating story is possible and has been done, but it very much outside the norms of early RPGs that arose primarily from how to handle combat and control single characters rather than navigate situations.
You might want to explore games like Primetime Adventures and Universalis. Those are very broad in scope. For a much more focused example, look at Fiasco or Durance. I once played a Durance game where we rolled up some pivotal turning point, in which the power dynamic had to suffer a violent disruption, and we had to map that into the characters & fiction we had going. Everybody was kinda stumped, until I said that my character (the warden), who was present on the scene, had to die right in that moment, sparking a riot, and everybody's eyes widened as they realized that was exactly the proper thing to happen for drama's sake—even though I was losing my character! But in fiction, people die, even the ones the author dearly loves. The warden had had a bunch of cool stuff happen up to then, but in the total picture of things, her death was the pivot point for the entire session and playing that out was immensely satisfying, for me and the rest of the table.
I switched to playing a prisoner pretty much at the bottom of the bottom in that very stratified social hierarchy and turned out a compelling story for him, too.
I've had less opportunity than I'd like to explore more recent games, but I bet some folks could chime in on developments since then.
With regard to the topic's focus on computer/video games, that would be much more difficult, for reasons already cited earlier in this thread.
