Games like Asylium
Games like Asylium include Poppy Playtime, Outlast, Amnesia: The Dark Descent, Inside the Backrooms, and SOMA. We matched them by the tags players give Asylium on Steam (Psychological Horror, Puzzle, Horror, Escape Room, and Stealth): closest matches first, and among equally close ones the better-known games.

Poppy Playtime
Shared: Horror · Puzzle · Psychological Horror

Outlast
Shared: Horror · Psychological Horror · First-Person

Amnesia: The Dark Descent
Shared: Psychological Horror · Horror · Puzzle

Inside the Backrooms
Shared: Horror · Puzzle · Psychological Horror

SOMA
Shared: Psychological Horror · Horror · Atmospheric

Escape the Backrooms
Shared: Horror · Psychological Horror · Escape Room

Little Nightmares II
Shared: Horror · Puzzle · Psychological Horror

Little Nightmares
Shared: Horror · Puzzle · Atmospheric

Lethal Company
Shared: Horror · First-Person · Psychological Horror

Garten of Banban
Shared: Horror · Psychological Horror · Puzzle

Layers of Fear (2016)
Shared: Psychological Horror · Horror · Atmospheric

Backrooms: Escape Together
Shared: Horror · Psychological Horror · Atmospheric

We Were Here
Shared: Puzzle · Escape Room · Horror

Bendy and the Ink Machine
Shared: Horror · Puzzle · First-Person

The Room Two
Shared: Puzzle · Horror · Atmospheric

Resident Evil 7 Biohazard
Shared: Horror · First-Person · Psychological Horror

The Outlast Trials
Shared: Horror · Psychological Horror · First-Person

Amnesia: Rebirth
Shared: Puzzle · First-Person · Horror

Outlast 2
Shared: Psychological Horror · Horror · First-Person

Sally Face - Episode One
Shared: Psychological Horror · Horror · Puzzle

ROUTINE
Shared: Psychological Horror · Atmospheric · Horror

Firework
Shared: Horror · Puzzle · Psychological Horror

Visage
Shared: Psychological Horror · Horror · First-Person

Penumbra Overture
Shared: Horror · Psychological Horror · First-Person

