I'm going to have to disagree with this, in part because it participates in the quote "all things are one things" end quote fallacy, where imagination must be limited to a single archetypical setting and nothing beyond that is considered worthwhile. You know, the dumbest possible interpretation of narrative.
But that out of the way first. A horror RPG only depends on the characters being horrified. Characters can only be horrified by things they see and recognize and know. Lovecraftian protagonists start knowing nothing of the mythos, and the horror escalates as they are exposed to it and begin to understand what it is that the things they see imply. A lot of military horror hinges on the protagonists not being powerless in a physical sense, but having that power be inapplicable to the things that they discover and interact with. (Zombies are largely resistant to bullets. Demons don't care about being shot, werewolves regenerate, etc.)
Many horror creators fixate too much on "characters should be powerless." This obviously is not necessary. In fact, it's often better if the characters have an element of power, which provides them a tool to interact with the world and for the horror to be manifest around.
Which brings us to psychics. What is psychic power in the context of many horror stories? It's a way for the characters to see things they would not otherwise see. The medium can see and talk to ghosts. The telepath can hear the thoughts which echo in people's dark impulses. The prescient can see the nightmares to come if they don't act, and perhaps if they do. The telekinetic has the ability to exert physical power, but that physical power may not be directly useful. All of the above can be opened to the powers of the horrors beyond through the use of their abilities in many settings.
Paranormal abilities represent just one more way for the characters to have their power rebuffed, diffused, or made dangerous. Just like guns, cell phones, and social groups, all of which have been called out in the past by inferior writers as detrimental to writing horror.
Is it appropriate to every setting? No, absolutely. If your story is about an extremely grounded group dealing with serial killers, then a group of psions might not be your best bet. On the other hand, that also sounds like it could be absolutely fucking amazing, done well.
The real secret is there is no secret to good writing. There's nothing to avoid. Just understand what it is you're doing and what the story requires. Everything else is catch as catch can.
Paranormal abilities for player characters in a horror RPG should be rare. Being psychic supermen/women makes PCs too similar to monsters.
Agree/disagree?