There are two stories it tells: the story of Aloy, the character you play, and the backstory of how the world she's in came to be. The former is a tribal/feudal fantasy story, and the latter is straight science fiction. Both are good, but I found the backstory
really compelling, with some great pull-the-rug-out-from-under-you twists. There's also some great character writing, generally delivered well; Nil the bloodthirsty bandit-hunter and Erend the mercenary were two of my favorites.
I actually just finished watching
a playthrough on YouTube; I can't remember why I started watching, but I was surprised to find I got completely sucked back into the world and the story, and really enjoyed watching the player's reactions to the plot as it unfolded. I fast-forwarded through the pure mechanics, but it's a little shocking how much of the 40-something-hour Let's Play I wound up watching.
The narrative director for the game was John Gonzales, who was heavily involved in (possibly also narrative director for, I'm not sure) Fallout: New Vegas. I never played enough of New Vegas to actually get to the story, and I now suspect that was a mistake. But more than that, I
really hope he's doing the unannounced-but-of-course-there-will-be-one sequel to Horizon, because I think he knocked it out of the park with the world, the story, and the characters.