Games like Empty Gauge
Games like Empty Gauge include What Remains of Edith Finch, Firewatch, No, I'm not a Human, SOMA, and Layers of Fear (2016). We matched them by the tags players give Empty Gauge on Steam (Psychological Horror, Horror, First-Person, Atmospheric, and Multiple Endings): closest matches first, and among equally close ones the better-known games.

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

Firewatch
Shared: Atmospheric · First-Person · Mystery

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

SOMA
Shared: Psychological Horror · Horror · Atmospheric

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

Amnesia: A Machine For Pigs
Shared: Horror · Psychological Horror · Atmospheric

MiSide
Shared: Psychological Horror · Horror · First-Person

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

Outer Wilds
Shared: Exploration · Mystery · Atmospheric

Outlast
Shared: Horror · First-Person · Psychological Horror

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

Mouthwashing
Shared: Psychological Horror · Horror · Atmospheric

Lethal Company
Shared: Horror · First-Person · Psychological Horror

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

SILENT HILL 2
Shared: Psychological Horror · Horror · Atmospheric

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

Iron Lung
Shared: Horror · Psychological Horror · Atmospheric

The Park®
Shared: Psychological Horror · Horror · First-Person

Little Nightmares
Shared: Horror · Atmospheric · Psychological Horror

Visage
Shared: Psychological Horror · Horror · First-Person

Little Nightmares II
Shared: Horror · Psychological Horror · Atmospheric

The Test
Shared: Psychological Horror · Multiple Endings · Simulation

Amnesia: The Dark Descent
Shared: Horror · Psychological Horror · Atmospheric

OMORI
Shared: Psychological Horror · Horror · Story Rich

