Games like That Which Gave Chase
Games like That Which Gave Chase include Outlast, Poppy Playtime, Firewatch, Layers of Fear (2016), and Blair Witch. We matched them by the tags players give That Which Gave Chase on Steam (Atmospheric, Horror, Dogs, First-Person, and Dark): closest matches first, and among equally close ones the better-known games.

Outlast
Shared: Horror · Atmospheric · First-Person

Poppy Playtime
Shared: Horror · First-Person · Singleplayer

Firewatch
Shared: Atmospheric · First-Person · Walking Simulator

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

Blair Witch
Shared: Horror · First-Person · Dogs

INSIDE
Shared: Atmospheric · Horror · Dark

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

Little Nightmares II
Shared: Horror · Atmospheric · Dark

Garten of Banban
Shared: Horror · First-Person · Singleplayer

Mouthwashing
Shared: Horror · Atmospheric · Dark

Resident Evil Requiem
Shared: Horror · First-Person · Action-Adventure

SOMA
Shared: Horror · Atmospheric · Dark

Hellblade: Senua's Sacrifice
Shared: Atmospheric · Horror · Dark

Little Nightmares
Shared: Atmospheric · Horror · Dark

ROUTINE
Shared: Atmospheric · Horror · Dark

Visage
Shared: Horror · Dark · Atmospheric

Bendy and the Dark Revival
Shared: Horror · First-Person · Singleplayer

Buckshot Roulette
Shared: Horror · Dark · First-Person

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

Among the Sleep - Enhanced Edition
Shared: Horror · Atmospheric · First-Person

Outlast 2
Shared: Horror · First-Person · Atmospheric

Slender: The Arrival
Shared: Horror · First-Person · Atmospheric

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

Choo-Choo Charles
Shared: Horror · First-Person · Dark