While not technically a horror game, the Scarecrow levels in Arkham Asylum are terrifying, a lot more so than any iteration of Scarecrow in Batman films.
The Arkham games do well to emulate the gritty DC comics better than Christopher Nolan ever did, and the sheer number of characters make them great fun to play through. However, the Scarecrow levels in particular are what qualify Arkham Asylum as a horror game.
After Scarecrow administers his fear toxin to Batman, the caped crusader begins to hallucinate memories of his parents' deaths, as well as a giant version of Scarecrow looking for him. These levels require Batman to keep out of sight, and shine Bat-Signals representing a manifestation of his willpower to blind and defeat Scarecrow.
The developers were genuinely original with their designs of such a well-known character, and used the fear toxin to good effect, scaring Batman and the player one and the same. They also did well to steer clear of previous representations of Scarecrow, and led the way for licensed games to be considered their own art form in themselves, rather than just extensions and copies of large corporations' existing products.