Games like The Wickers House
Games like The Wickers House include SOMA, Mouthwashing, No, I'm not a Human, Still Wakes the Deep, and Layers of Fear (2016). We matched them by the tags players give The Wickers House on Steam (Horror, Atmospheric, Psychological Horror, Story Rich, and Detective): closest matches first, and among equally close ones the better-known games.

SOMA
Shared: Horror · Atmospheric · Psychological Horror

Mouthwashing
Shared: Horror · Psychological Horror · Atmospheric

No, I'm not a Human
Shared: Horror · Psychological Horror · Atmospheric

Still Wakes the Deep
Shared: Horror · Psychological Horror · Gore

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

Outlast
Shared: Horror · Atmospheric · Psychological Horror

What Remains of Edith Finch
Shared: Atmospheric · Story Rich · Walking Simulator

Firewatch
Shared: Atmospheric · Story Rich · Walking Simulator

MiSide
Shared: Psychological Horror · Horror · Story Rich

Amnesia: A Machine For Pigs
Shared: Horror · Atmospheric · Story Rich

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

Resident Evil 7 Biohazard
Shared: Horror · Atmospheric · Gore

Outlast 2
Shared: Horror · Psychological Horror · Atmospheric

Little Nightmares
Shared: Horror · Atmospheric · Story Rich

Tiny Bunny
Shared: Horror · Atmospheric · Story Rich

Call of Cthulhu®
Shared: Horror · Psychological Horror · Atmospheric

SILENT HILL 2
Shared: Horror · Psychological Horror · Story Rich

Little Nightmares II
Shared: Horror · Atmospheric · Psychological Horror

>observer_
Shared: Horror · Psychological Horror · Atmospheric

Lethal Company
Shared: Horror · Psychological Horror · Atmospheric

Lobotomy Corporation | Monster Management Simulation
Shared: Psychological Horror · Horror · Story Rich

Fears to Fathom - Ironbark Lookout
Shared: Horror · Atmospheric · Psychological Horror

Fran Bow
Shared: Psychological Horror · Horror · Story Rich

The Vanishing of Ethan Carter
Shared: Atmospheric · Detective · Horror