Games like Insight
Games like Insight include Mouthwashing, SOMA, OMORI, Still Wakes the Deep, and No, I'm not a Human. We matched them by the tags players give Insight on Steam (Story Rich, Thriller, Horror, Detective, and Lovecraftian): closest matches first, and among equally close ones the better-known games.

Mouthwashing
Shared: Story Rich · Horror · Psychological Horror

SOMA
Shared: Horror · Story Rich · Psychological Horror

OMORI
Shared: Story Rich · Psychological Horror · Pixel Graphics

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

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

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

FAITH: The Unholy Trinity
Shared: Horror · Story Rich · Pixel Graphics

Call of Cthulhu®
Shared: Horror · Lovecraftian · Detective

Phasmophobia
Shared: Horror · Psychological Horror · Detective

INMOST
Shared: Story Rich · Pixel Graphics · Thriller

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

Fran Bow
Shared: Story Rich · Horror · Psychological Horror

MiSide
Shared: Story Rich · Horror · Psychological Horror

DISTRAINT: Deluxe Edition
Shared: Horror · Story Rich · Psychological Horror

Detention
Shared: Horror · Story Rich · Psychological Horror

Demonologist
Shared: Horror · Psychological Horror · Dark

Dagon: by H. P. Lovecraft
Shared: Horror · Lovecraftian · Story Rich

Little Nightmares II
Shared: Horror · Story Rich · Dark

Notch - The Innocent LunA: Eclipsed SinnerS
Shared: Story Rich · Horror · Thriller

The Test
Shared: Story Rich · Pixel Graphics · Psychological Horror

INSIDE
Shared: Story Rich · Horror · Dark

Alan Wake
Shared: Story Rich · Horror · Thriller

Layers of Fear (2016)
Shared: Horror · Story Rich · Psychological Horror

Inscryption
Shared: Story Rich · Horror · Dark