Games like Delirium
Games like Delirium include MiSide, No, I'm not a Human, Layers of Fear (2016), Outlast, and Mouthwashing. We matched them by the tags players give Delirium on Steam (Indie, First-Person, Psychological Horror, Atmospheric, and Singleplayer): closest matches first, and among equally close ones the better-known games.

MiSide
Shared: Psychological Horror · First-Person · Story Rich

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

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

Outlast
Shared: First-Person · Atmospheric · Psychological Horror

Mouthwashing
Shared: Psychological Horror · Indie · Atmospheric

SOMA
Shared: Psychological Horror · Atmospheric · Horror

Poppy Playtime
Shared: First-Person · Singleplayer · Horror

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

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

Five Nights at Freddy's
Shared: Singleplayer · Indie · Psychological Horror

Firewatch
Shared: Atmospheric · First-Person · Story Rich

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

Five Nights at Freddy's 2
Shared: Singleplayer · Psychological Horror · Horror

Sally Face - Episode One
Shared: Indie · Psychological Horror · Story Rich

Little Nightmares
Shared: Atmospheric · Horror · Singleplayer

In Sound Mind
Shared: Psychological Horror · Horror · Story Rich

Amnesia: A Machine For Pigs
Shared: First-Person · Atmospheric · Horror

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

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

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

Little Nightmares II
Shared: Singleplayer · Horror · Atmospheric

The Beginner's Guide
Shared: Indie · First-Person · Story Rich

Blair Witch
Shared: Indie · Psychological Horror · First-Person

Penumbra Overture
Shared: First-Person · Indie · Horror