There's no getting around role-playing game settings/backgrounds/backdrops contain plot, or rather, the seeds of potential plots. Good setting design (heck even most bad setting design) is a kind of plotting. Ergo, the DM must be more than just the art director. They are, at least in part, screenwriters.
There is no need for them to be either. My point in bring up 'art direction' was mostly to complicate any attempt at making an analogy. It wasn't to say that campaign settings were actually analogous to the art direction for a movie.
Why must we hammer the square peg of gamemastery (surely a square peg) into the round hole of screenwriting? We don't insist on labeling novelists screenwriters? Writing for a comic book and writing for the screen have alot in common, but we don't insist on calling comic book writers screenwriters.
Creating for an RPG is its own unique art and has its own unique needs and constraints. Good RPG art - and I mean the entire range of RPG art here not just visual art and illustration - has its own unique voice and needs that are unlike any other medium. A comic book has a writer, illustrator, inker, letterer, and editor each with there own impact on the finished work and each with their own role which is in many respects unique to the artform. For an RPG session, we have things like setting designer, a module writer, a gamemaster, and one or more players each of which contribute to the art. The gamemaster is not a director. The player is not an actor. They have roles that are different than those of the film and stage. In stage craft, the director tells the actor how to act, what to say, and where to say it in order to fulfill the director's artistic vision. Some director's allow the actor more freedom to experiment than others, but ultimately the director has authority over the players performance and that is the director's main role. In an RPG, the gamemaster is as much of an actor as the players themselves, and while his authority is greater even than that of a director, his authority over the performance of the other players is quite limited.
A role playing game is a role playing game. It shares some common features with movie making and novels and comic books by virtue of belonging to the same superclass, just as a tricycles, escalators, zeppelins, space shuttles, and cement mixers share some common features by virtue of being forms of transportation. However, just as we'd be idiots to insist on an analogy between the rotating drum of a cement mixer and some feature of an escalator, so we also gain very little by taking features unique to one form of story-telling (the director's role in a movie) and trying to make them analogous to all forms of story-telling.