Games like The Demon Within Me
Games like The Demon Within Me include Phasmophobia, MiSide, Outlast, Outlast 2, and Poppy Playtime. We matched them by the tags players give The Demon Within Me on Steam (First-Person, Horror, Psychological Horror, Atmospheric, and Supernatural): closest matches first, and among equally close ones the better-known games.

Phasmophobia
Shared: Horror · Psychological Horror · First-Person

MiSide
Shared: Psychological Horror · Horror · First-Person

Outlast
Shared: First-Person · Horror · Atmospheric

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

Poppy Playtime
Shared: Horror · First-Person · Psychological Horror

SOMA
Shared: Horror · Psychological Horror · Atmospheric

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

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

Mouthwashing
Shared: Horror · Psychological Horror · Atmospheric

Layers of Fear (2016)
Shared: Horror · Psychological Horror · First-Person

The Mortuary Assistant
Shared: Horror · Supernatural · Atmospheric

Garten of Banban
Shared: Horror · First-Person · Psychological Horror

Little Nightmares II
Shared: Horror · Atmospheric · Psychological Horror

Still Wakes the Deep
Shared: Horror · Psychological Horror · First-Person

Little Nightmares
Shared: Horror · Atmospheric · Dark

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

Five Nights at Freddy's
Shared: Horror · Psychological Horror · First-Person

Visage
Shared: Horror · Psychological Horror · First-Person

Buckshot Roulette
Shared: Horror · First-Person · Dark

Amnesia: The Dark Descent
Shared: Horror · Psychological Horror · First-Person

What Remains of Edith Finch
Shared: Atmospheric · First-Person · Story Rich

Resident Evil Village
Shared: Horror · First-Person · Singleplayer

Firewatch
Shared: Atmospheric · First-Person · Story Rich

From The Darkness
Shared: Horror · Psychological Horror · First-Person