The Shining is certainly a flavor of horror. I think part of the problem of trying to make a list where the only criteria is horror sweeps up such a broad array of movies. Like Hostel, From Beyond, Alien, and Silence of the Lambs are all equally in the same bucket, which doesn't seem right.
There are a lot of way to sort the distinctions, but The Shining is deserving of a slot somewhere in the realm of supernatural horror. It relies on creepy atmosphere and a descent into isolation with audience along with the characters, more than blood splattering, or some kind existential question to shake the audience. It is, at its core, a haunted house movie.
I have a hard time categorizing Stuart Gordon movies as horror (I suppose technically that's where they end up). They have horror trappings, but everything is so theatrical that it doesn't really scan as scary. It's not a failing either but more like the intentional tone.
The closet modern analog would be maybe Slither? It's incredibly gross and has concepts that would be horrific to experience, but I'm so removed as an audience member that it's really just more fun being grossed out.
Invasion of the body snatcher is the movie i watched when i was like 8 at a friends house. After that i had to walk home by myself at night. I never ran that fast home and never felt that scared, in kind of a good way. I never felt like that again and i'm not super into horror movies anyway, but that must be what junkies talk about when they say they chase that first "high" except for horror movies. A few years ago i discovered the band wolfie's just fine, and their song reminded me a lot of that experience.
https://youtu.be/qG8iAtpavK4?si=7bIu109xXBdY68aG
I caught the original b&w version when I was about the same age, spent a month checking under the bed for pods. I feel you!
I think it's a generational thing too... there have been so many versions of that story it can hit everyone:
The original was 1956. Then the remake in 1978. "Body Snatchers" in 1993 which is creepy as hell, and apparently "The Invasion" in 2007 which I somehow missed.