Games like BURN
Games like BURN include Mouthwashing, No, I'm not a Human, SOMA, What Remains of Edith Finch, and Hellblade: Senua's Sacrifice. We matched them by the tags players give BURN on Steam (Psychological Horror, Story Rich, Horror, Atmospheric, and Retro): closest matches first, and among equally close ones the better-known games.

Mouthwashing
Shared: Psychological Horror · Story Rich · Horror

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

SOMA
Shared: Psychological Horror · Horror · Story Rich

What Remains of Edith Finch
Shared: Story Rich · Atmospheric · Psychological Horror

Hellblade: Senua's Sacrifice
Shared: Atmospheric · Story Rich · Psychological

MiSide
Shared: Psychological Horror · Story Rich · Horror

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

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

Outer Wilds
Shared: Story Rich · Atmospheric · Space

Fears to Fathom - Norwood Hitchhike
Shared: Psychological Horror · Horror · Atmospheric

Firewatch
Shared: Story Rich · Atmospheric · Adventure

Little Nightmares II
Shared: Horror · Psychological Horror · Atmospheric

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

Fran Bow
Shared: Psychological Horror · Story Rich · Horror

Poppy Playtime
Shared: Horror · Psychological Horror · Dark

Outlast
Shared: Horror · Psychological Horror · Atmospheric

Little Nightmares
Shared: Horror · Atmospheric · Story Rich

Detention
Shared: Psychological Horror · Horror · Atmospheric

Alan Wake
Shared: Story Rich · Horror · Psychological Horror

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

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

Outlast 2
Shared: Psychological Horror · Horror · Atmospheric

Still Wakes the Deep
Shared: Psychological Horror · Horror · Story Rich

The Cat Lady
Shared: Story Rich · Horror · Psychological Horror