I’ve never run a horror game, but I have seen people at tables become unsettled or freaked out.Two things disabused me of this notion. First was reading more horror and realizing that scares weren't actually the core fo the genre. The core of the genre, it seems to me, is being unsettling. And you certainly can do that in a TTRPG.
One night, the group wanted me to run a classic metal soundtrack to our weekly game. So I selected some CDs and hit shuffle. That evening, just as our party was entering a graveyard, Black Sabbath’s “Children of the Grave” popped up by coincidence. Now, the “grave” in that song is allegorical, and everyone at the table knew that. But it nonetheless set the players on edge.
At a different time, I deliberately used Kodo’s “The Hunted” as the signal that the big game hunt for the party was officially underway. I immediately heard stress-related changes in pitch, volume, and speed in the players’ voices when they realized why I was playing that composition; that what they were hearing was what their characters were hearing.