For example, when I am running a situation, I don't care if it is a 'good scene' in the sense that you have in a film.
I object that you do.
All I care about is if the game is fun.
Is that what the movie maker ultimately cares about as well? I mean, even a horror movie maker that wants to inflict scares, or a dramatists that wants to provoke tears in a scene, ultimately wants to do that because at some level the audience enjoys that experience and came to the movie to experience it. I don't see this distinction as a distinction at all. If all you care is that the game is fun, then you do care about having good scenes. What makes the scene good is that it is fun.
And part of the game being fun, at least for many of my groups, is making sure the players have a sense that they are interacting with a breathing setting that isn't always oriented around their personal drama or character arc (like you have in a movie).
You have an excessively narrow view of movies, personal drama, or character arc. It's perfectly fine to have a movie where there protagonist is experiencing some breathing setting that doesn't revolve around them. Plenty of movie makers try to capture the experience of actually being peripheral to the events of the story either as the audience or the characters of the story, and for the events of the story to be essentially random and meaningless on the grounds that the movie maker perceives this to be how life goes.
In a movie Chekov's gun stands. In an RPG I don't think it does. In a movie, scenes ought to be efficient and lead naturally to the next scene. In an RPG there is a lot of back and forth, deliberation, etc. In a movie a scene needs to move in a certain rewarding direction. In an RPG, it is a game, and the dice determine many outcomes. There is a natural conflict between that and the dramatic needs of a movie scene.
Yeah, I'm just not getting this. You've got a simplified stereotype of a movie you are fighting against, and yet ultimately movies are about entertainment. And there is no formula for what entertains an audience.
And in any event, I have defined 'scene' for the purpose of an RPG without reference to a movie 'scene'. So while there is an obvious relationship, no one is or should be surprised if what makes a good scene in an RPG is not exactly the same as what makes a good scene in a movie. No one should be particularly surprised if there is some overlap, but there is no reason that anything that applies to a movie needs to apply to an RPG. That's not generally what an analogy is in the way most people use analogies, nor for that matter am I using analogy since I tend to think analogies confuse people more than they clarify. When most people use an analogy, they are normally stating only that two things share a limited set of features. They are not normally insisting that for every feature of the first thing, there exists a one to one and onto mapping to features of the second thing. Tolkien famous asserted that because people tended to assume from analogies that this was true, when it obviously was not, that people shouldn't use analogies at all. Whatever relationship between scenes in the story telling medium of an RPG that I'm drawing with scenes in a movie, it is certainly not a one to one and onto mapping.
As for Chekov's Gun, I've used it in an RPG several times to great success. I think you are trying to say that since an RPG has a branching story path (at least potentially) stories can be abandoned if the protagonists lose interest in them, and as such the Chekov's Guns of that story will never be fired, or perhaps will be fired, but will be fired offstage when the protagonists are no longer around to hear or even learn of their firing. And while that's true, I'll still insist that the very fact you are aiming to have a world that fills living and breathing means that those Chekov's Guns will tend to be fired by someone, because otherwise it wouldn't feel living and breathing.
My favorite Chekov's Gun concerned the neighbor of one of the PCs, an undertaker, introduced in basically Act II, Scene 1 of the story, helping the PCs collect the dead after a natural disaster. That gun didn't get fired for about 2 years of gaming, but when it went off, oh boy was it a good one.