Horror stories affect audiences by putting a likeable, relatable person in a cruel and unfair position with little power to escape. The "horror" comes from bad things happening to people ostensibly like us. Movies show us these people, books dictate their thoughts and feelings. Each time the object of fear strikes, the threat comes closer. Games don't need to work that way because the player is in direct control of the protagonist. Even if the avatar is a separate personality, by virtue of directing their action, the player and the protagonist are one.
The relationship between player and protagonist extends past the player, horror games also engage passive audience members sharing the couch with the player. The participatory role of the player is augmented by the passive advice of the audience. Telling a character in a movie that the killer is just on the other side of that door does nothing. But in a game, the character (the player) can respond, heeding or ignoring the audience's advice. The tension, the bursts of action and the relief are all intensified with a spectator. Even without the controller a spectator has an impact on the game's events. Similarly, without experiencing the game first hand, the spectator can become invested in the game through their relationship with the player.
No other genre is as well suited for spectator-ship as horror games. Puzzle games often lack the urgency and action games lack the emotional weight. Horror is a universal experience and the narrative technique of games is excellently suited to deliver it. We can't help but get invested in the fate of our friend as they sprint for a safehouse or trickle their last store of ammo into an endless wave of monsters.
Even viewers with no interest in video games can recognize their aesthetic significance can impact the senses in unique ways. No game's impact is more visceral on viewers than a horror game's. Everyone can identify with fear, regardless of whether or not they play games. There are plenty of games that must be played to be fully appreciated, but horror games are actually often better played with a full couch.