The narrative aspect of The Stanley Parable is probably the most unique part of the game, not because it is literally narrated to us by some omnipotent voice, it is the fact that the player can choose to obey or defy what the narrator tells them to do, and furthermore, the narrator reacts to the player’s choices. This is what makes this such a pure video game experience. In most cases where there is a narrative element, the spectator cannot deviate from the narrator; and every time we revisit said experience, it is in the same perspective it was done the time before (arguably, one can say that the context can affect in some ways the narrative experience, but the plat shall remain the same and the elements which construct it will do in the same way). In this game, on the other hand, the player can reach multiple endings, even the paths to said endings can differ from playthrough to playthrough, which is the main difference in regards to narrative in other media, since it sheds linearity in favour of multiple branching paths, it gives the spectator a choice.
The figure of the narrator is particularly interesting in the studied game, since he is not a conventional narrator by any means. This is most noticeable in the fact that the narrator adapts to the player, which is a physical impossibility in any other medium, because they are done in a certain way and they remain that way. The narrator of The Stanley Parable makes fun of some of the decisions the player makes, interacts with the player, and most importantly becomes a factor in the story. What I mean by this is that the narrator of this game is heterodiegetic, which means he is an entity that exists outside of the story and depending on how the player goes about obeying or disobeying the narrator he can be either an antagonistic force or an ally for the player.
Another interesting aspect of the narrative in The Stanley Parable is that it is built almost entirely by the games paidea rules, since the game has no clear ludus rules (main objectives or goals, there is no main objective to pursue nor one established ending) the paidea and ludus rules intertwine and en end up making obeying the narrator or not the only way to move the plot of the game forward, and thus the fabula of the game is constructed by the actions and vice versa.
The main objective in the narrative here is to have no apparent order, the player can experience The Stanley Parable as he or she wishes to, there is no definitive guide to this game. And there is no real end.