I think there is a meaningful description between "story as a natural byproduct of things happening in a sequential order" and "story as an interesting narrative that can stand on its own merits, separate from the process of play".
Because, well, not only game mechanics inherently tell stories. Everything inherently produces a story. Not everything produces a story that is worth sharing.
Ah, but thats the rub! Game stories are worthy enough to stand on their own as a "new" form of narrative.
New is in quotes because we've been observing the potential for about as long as we started doing competitions in general, we just don't conventionally recognize those narratives in the same way as we do a book or a film.
Borg vs McEnroe. The Miracle on Ice. Game 7 of the 1960 World Series. Game 3 of the 1932 World Series when Babe Ruth called his shot. And so on and so on.
These stories can only exist because of the game and metagame they centered on, and they're just as compelling to follow as any book or film, especially more recent ones as we can now much more readily reconsume them as they were rather than secondhand. Sports fans can, like any other fan of any other medium, get so into the weeds with their mediums jargon that it obscures what they're really there for, but there is a reason why the Highlights is a thing on sports TV, and it isn't just because its just neat to see peak athletes do their thing.
And with streaming, we're seeing this kind of narrative come into its own as video game streamers are some of the most popular entertainment out there. The game being intermixed with the metagame formed by the streamers persona is compelling enough to be entertaining.
And I don't think we even need to wait to see this evolve into something more deliberate as an art; Me, Myself, and Die is basically a prime example of exactly that, where the game and metagame are pursued towards that end.