There's no terror if there's no penalty for failure
Most video games are structured in such a way that the player character's life is in danger. You can die by falling from a platform, or getting gunned down by your enemies, or being eaten by monsters.
So what separates a horror game from any other? Horror games alter the relationship between player and game through two mechanisms: they balance combat to be unfavorable to the player, and they contextualize the gameplay in the conventions of the horror genre (minimal lighting, grim imagery, ominous music, etc).
Amnesia: The Dark Descent has been lauded as one of the best examples of horror gaming. It uses Lovecraftian imagery to great effect, and the combat is decidedly unfavorable to the player. In fact, Amnesia's main innovation is that the player has no way of engaging in combat at all. When confronted with an enemy NPC you can either hide or die.
But the illusion breaks completely once you realize that death has no penalty. When confronted with a monster the optimal play strategy is to simply walk up to it, let it kill you, and restart the sequence. When you respawn the monster will no longer be there. You lose neither items nor progress, and the story is unaffected.
In other words, to achieve horror Amnesia (and most games in the genre) relies on the player's willingness to be immersed in a core fiction: that the game's danger is real. This is in contrast to a game like Heavy Rain, where gameplay failure may have a permanent effect on the outcome of the narrative. For me, this was where Amnesia failed. It was too easy to choose not to be scared, to treat it as a puzzle game in a moody setting. If you're willing to suspend your disbelief, you may get far out of the game.