Games like Amnesia: Rebirth
Games like Amnesia: Rebirth include Little Nightmares II, Poppy Playtime, SOMA, Bendy and the Dark Revival, and Five Nights at Freddy's: Security Breach. We matched them by the tags players give Amnesia: Rebirth on Steam (Action-Adventure, First-Person, Puzzle, Story Rich, and Singleplayer): closest matches first, and among equally close ones the better-known games.

Little Nightmares II
Shared: Puzzle · Horror · Singleplayer

Poppy Playtime
Shared: Puzzle · First-Person · Singleplayer

SOMA
Shared: Horror · Story Rich · First-Person

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

Five Nights at Freddy's: Security Breach
Shared: First-Person · Singleplayer · Horror

Indiana Jones and the Great Circle
Shared: Action-Adventure · First-Person · Puzzle

Little Nightmares
Shared: Horror · Singleplayer · Puzzle

Portal 2
Shared: Puzzle · First-Person · Singleplayer

What Remains of Edith Finch
Shared: Story Rich · First-Person · Singleplayer

Amnesia: The Dark Descent
Shared: Horror · Puzzle · First-Person

Bendy and the Ink Machine
Shared: First-Person · Puzzle · Horror

Hello Neighbor 2
Shared: Puzzle · First-Person · Action-Adventure

Rise of the Tomb Raider™
Shared: Adventure · Singleplayer · Action-Adventure

Outlast
Shared: First-Person · Horror · Singleplayer

Outer Wilds
Shared: Story Rich · Exploration · Puzzle

Tomb Raider Game of the Year
Shared: Adventure · Singleplayer · Story Rich

Firewatch
Shared: Story Rich · First-Person · Adventure

Resident Evil 7 Biohazard
Shared: First-Person · Horror · Singleplayer

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

Penumbra Overture
Shared: First-Person · Horror · Adventure

UNCHARTED™: Legacy of Thieves Collection
Shared: Action-Adventure · Story Rich · Adventure

Penumbra: Black Plague Gold Edition
Shared: First-Person · Horror · Adventure

Resident Evil Village
Shared: First-Person · Horror · Singleplayer

Metro Exodus
Shared: Singleplayer · Story Rich · First-Person