Games like Gate to Site 8
Games like Gate to Site 8 include Mouthwashing, What Remains of Edith Finch, SOMA, Layers of Fear (2016), and Firewatch. We matched them by the tags players give Gate to Site 8 on Steam (Story Rich, Psychological, Dark, Horror, and Psychological Horror): closest matches first, and among equally close ones the better-known games.

Mouthwashing
Shared: Story Rich · Horror · Psychological Horror

What Remains of Edith Finch
Shared: Story Rich · Walking Simulator · Atmospheric

SOMA
Shared: Story Rich · Horror · Psychological Horror

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

Firewatch
Shared: Story Rich · Atmospheric · Walking Simulator

Amnesia: A Machine For Pigs
Shared: Story Rich · Horror · Walking Simulator

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

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

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

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

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

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

Fran Bow
Shared: Story Rich · Psychological Horror · Horror

Layers of Fear 2 (2019)
Shared: Horror · Psychological Horror · Story Rich

Blair Witch
Shared: Horror · Psychological Horror · Dark

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

God's Basement
Shared: Horror · Dark · Psychological Horror

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

Little Nightmares II
Shared: Horror · Dark · Story Rich

MiSide
Shared: Story Rich · Psychological Horror · Horror

Little Nightmares
Shared: Horror · Dark · Atmospheric

Outlast
Shared: Horror · Psychological Horror · Atmospheric

The Medium
Shared: Horror · Story Rich · Psychological Horror

Visage
Shared: Horror · Dark · Psychological Horror