Games like The Repairing Mantis
Games like The Repairing Mantis include Firewatch, What Remains of Edith Finch, Mouthwashing, SOMA, and Layers of Fear (2016). We matched them by the tags players give The Repairing Mantis on Steam (Exploration, Horror, Walking Simulator, Psychological Horror, and Adventure): closest matches first, and among equally close ones the better-known games.

Firewatch
Shared: Adventure · Walking Simulator · Atmospheric

What Remains of Edith Finch
Shared: Walking Simulator · Exploration · Atmospheric

Mouthwashing
Shared: Horror · Psychological Horror · Atmospheric

SOMA
Shared: Horror · Psychological Horror · Atmospheric

Layers of Fear (2016)
Shared: Horror · Psychological Horror · Walking Simulator

Amnesia: A Machine For Pigs
Shared: Horror · Walking Simulator · Exploration

Still Wakes the Deep
Shared: Horror · Psychological Horror · Walking Simulator

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

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

Outer Wilds
Shared: Exploration · Adventure · Story Rich

The Park®
Shared: Horror · Walking Simulator · Psychological Horror

Gone Home
Shared: Walking Simulator · Exploration · Atmospheric

Lethal Company
Shared: Horror · Exploration · First-Person

Outlast
Shared: Horror · Psychological Horror · Atmospheric

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

Visage
Shared: Horror · Psychological Horror · Atmospheric

Blair Witch
Shared: Horror · Psychological Horror · Adventure

INFRA
Shared: Exploration · Walking Simulator · Atmospheric

MiSide
Shared: Psychological Horror · Horror · Story Rich

Scanner Sombre
Shared: Exploration · Horror · Walking Simulator

The Beast Inside
Shared: Horror · Adventure · First-Person

CARIMARA: Beneath the forlorn limbs
Shared: Exploration · Horror · Story Rich

The Beginner's Guide
Shared: Walking Simulator · Story Rich · Atmospheric

THRESHOLD
Shared: Horror · Psychological Horror · Exploration