I think there are supernatural elements to the Shining, but that they aren't the horrifying element. Yes, Danny's Shining ability lets him see all manner of screwed up scenes, giving him the clear feeling that something's not right. Yes, the ghosts play the father like a piano, using his alcoholic tendencies, familial frustrations, and professional letdowns to wind him up like a toy soldier and send him off on everyone in a mile radius. There is a lot of supernatural elements at play.

But the horror isn't supernatural. The Shining isn't meant to terrify, it's meant to unsettle. The horrifying thing is watching a clearly flawed but worryingly realistic father figure get twisted more and more until he hunts his own family down with a butcher knife and a fire ax, laughing and referencing late night television memes as he does it. And since you've spent the movie unsettled, it makes watching this truly mundane horror of a broken paternal figure turned implacable killer that much more brutal.

Does it work? Probably not so much, anymore. People look at the Shining elements and brush them off as cheap scares, setting a stage of jaded disappointment instead of mounting discomfort. But I believe it did work at the time.