My point is that when a story emerges from play, by definition that story (the tale of our band of weirdos liberating gold from a dragon's hoard, for example) is not complete until the game reaches some sort of resolution.I think that RPGs occupy a middle ground between story and game because the two are intertwined. The story is emerging through play, but sometimes it’s set up in advance, and sometimes it’s retroactively applied based on choices that were made during the game. I think there’s some emphasis being placed upon the completion of the story, and I’m not sure I’m comfortable with that being an important part of the definition. If a book or TV show is left incomplete, does it no longer qualify as a story? If an author leaves a story intentionally incomplete, and leaves it to the reader to make the final determination, is it not still a story?
When we play a game, we’re in the process of creating that story. I don’t know if there’s a tremendous amount of value for me to separate the act of creating a story from saying what results is a story. The similarities are greater than the differences to my mind. I don’t think there’s very many games that I’ve played where I didn’t complete the story in my mind even if it didn’t fully play out at the table, say due to a campaign that ended prematurely. I tend to imagine what the ending would’ve been and that’s enough for me.
But what I am really trying to express is that when we play, we aren't in a sotry following a plot and acting in a coherent way meant to evoke Story. We are playing a game. Because of the nature of RPGs, that means we produce a story in that play.
Now, there are games that want you to play within a story. Modules from the 90s are a common offender in this regard, but even things like the "cinematic" adventures for Alien do something similar. And of course there are storygames whose sole purpose is to envelop the participants in story as part of play. But in all of those examples, it is necessary to restrict some choices that would otherwise be available to the players in order to force story beats and structure.

