I would put it a bit differently.
There is a type of human creative endeavour called storytelling. It includes certain elements which can be understood at least semi-technically: characters who have dramatic needs; rising action; perhaps most importantly crisis or climax in which the question of whether the character will fulfil their dramatic need is posed and answered; and, as a result, resolution one way or another.
The appeal of RPGing, for me at least, is that it enables the creation of stories with (i) no one having to be the storyteller, and (ii) the possibility of having the experience of "being" the character. This is a distinctive type of aesthetic experience.
Key to achieving (ii) is to have PC build establish dramatic needs for those PCs. These are the player priorities that I have talked about in this thread. And I've said a bit about how various RPG systems permit players to express them (eg player-authored quests in 4e D&D).
Key to achieving (i) is to have a system for framing, and for resolution, that will make dramatic need salient without anyone have to choose, in advance, what the resolution of those needs will look like. I've given examples, and explanation, that show how certain GMing principles can achieve this. (There are other RPGs with principles that are a bit different from what I've discussed that can also do this, most prominent Apocalypse World and some of its offshoots.)
The alternative approach being set out in this thread, in which players play characters who are to a significant extent self-inserted lenses whereby they learn what the GM has in mind for the fiction, and prompt the GM to present and develop those ideas, is to me a quite different experience. It involves comparatively less creative engagement from the players. Their role is to provide characterisation for their PCs, and to unravel the "mystery" of the GM's world - to work out how it operates, what its various components are and how they related, etc. Players, in this approach, perform a role that is more cognitive than creative.
Right, so for example I ran Agon for a couple of my friends last night, a game which
@pemerton you are fairly well-versed. Thematically this game is one in which a boatload of Greek Heroes sail an abstract sea full of islands. Each episode features landing on an island, solving its conflicts and answering its mysteries. Mechanically its a pretty straight up dice pool (roll some, take the best 1 or 2) resolution system. The GM describes the current situation, the PCs act, and when they conflict with a 'worthy opponent' (which can be things like storms, puzzles, etc. not always an NPC or faction) a 'Conflict' is created, which is adjudicated by a single throw of dice by the GM and each participating hero.
While the islands present a scenario, a situation laden with potential for conflict, and in which the gods have an interest, there are no really established sequences of events nor things like maps or such. A couple key locations will be described in a paragraph each, at most, along with 2-4 characters/factions that are party to the island's conflict.
So, this game is exceedingly loose in construction, but very tightly specified in thematic terms, and the overall shape of play is fairly set. The PCs will voyage (sort of a recovery phase where they increase their resources), pick a Leader via an initial "us against the world" kind of contest, and then the GM gives them 'signs from the gods' related to the next island, and they 'land' (which may not actually involve literally landing the ship). An initial scene is described which will normally give the PCs a couple options of obvious paths to follow. For instance one island, Vrachoi, gives the PCs the immediate choice to befriend one of two warships and their associated faction (presumably you could switch sides later perhaps, but NOW you must make some sort of choice).
Kryos gives the PCs two choices that are spelled out, command Meletia (the mayor basically) to rebuild a temple to Hera, or command Ionestes, the priest of Hera, to stop promising non-existent divine aid and create some practical defenses. The intro scene establishes that the island's magical defenses have been lost and harpies will soon come and kill the people. Something has to be done!
Well, my players didn't seem to care too much for the obvious choices, they began to investigate the theft of the magic defenses (the pillar of storms, part of the Hera temple). Pretty soon the lead hero got tired of talking (being a 'Blood & Valor' type), found out where the harpies live, and mustered the people to go wipe them out! She was successful in getting this plan enacted. Now, this is enabled GAME-WISE by the fact that the players are in charge of reciting their deeds once the dice have been tossed. They have to do so within the parameters suggested by which dice they used (IE if you invoke a bond with another hero, that has to be explained in the recitation, as would the favor of a god, etc.). Even if the PCs lose, the heroes still recite their deeds, they just have to recite FAILURE, and the GM gets to describe what the opponent does (if the heroes win that just means describing what its defeat looks like). Thus the overall consequences and how the contests shape the ongoing fiction is at least 50% up to the players. They get to say what resources they commit (the stakes) and what the outcome looks like, as long as it fits with the established fiction.
So, the players determine the nature of their heroes (which gods they revere, which domains they have their dice in, etc.) and the GM sets the parameters of the overall conflict they will be involved in, and generally the NPCs, etc. Then the players, mostly, decide when and where, and why, and how, to engage in contests in order to resolve the island's strife. I guess if the PCs turtle or entirely ignore the island's problems then the GM can confront them with contests. So there's some give and take as far as control of the narrative goes, its certainly not ENTIRELY in the player's hands, they're expected to work within the basic outline.
Remember, though, each island is, at most, about 750 to 1000 words, they're not big elaborate productions involving a lot of established detail. Nor is this really an exploration game, as such. While the players will need to discover SOME things in play, the basic outline of the situation and the strife involved is not exactly meant to be a big mystery. Also, as a general rule the players are not usually FORCED to enter a contest, they can decide if they're going to 'fight' now or change tactics and do something else.