Games like The Initiate
Games like The Initiate include Little Nightmares, Little Nightmares II, Sally Face - Episode One, Outer Wilds, and Brothers - A Tale of Two Sons. We matched them by the tags players give The Initiate on Steam (Indie, Adventure, Action, Puzzle, and Atmospheric): closest matches first, and among equally close ones the better-known games.

Little Nightmares
Shared: Adventure · Atmospheric · Horror

Little Nightmares II
Shared: Adventure · Horror · Puzzle

Sally Face - Episode One
Shared: Indie · Adventure · Story Rich

Outer Wilds
Shared: Adventure · Atmospheric · Puzzle

Brothers - A Tale of Two Sons
Shared: Adventure · Indie · Atmospheric

OneShot
Shared: Indie · Story Rich · Atmospheric

Fran Bow
Shared: Puzzle · Adventure · Indie

Detention
Shared: Indie · Horror · Puzzle

Ori and the Will of the Wisps
Shared: Action · Adventure · Singleplayer

Poppy Playtime
Shared: Horror · Puzzle · Singleplayer

Seen
Shared: Indie · Adventure · Puzzle

Firewatch
Shared: Adventure · Atmospheric · Story Rich

Alan Wake
Shared: Action · Adventure · Horror

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

Bendy and the Ink Machine
Shared: Horror · Puzzle · Singleplayer

Bendy and the Dark Revival
Shared: Action · Horror · Adventure

GRIS
Shared: Indie · Atmospheric · Adventure

INSIDE
Shared: Atmospheric · Indie · Horror

A Plague Tale: Innocence
Shared: Adventure · Story Rich · Atmospheric

What Remains of Edith Finch
Shared: Atmospheric · Adventure · Story Rich

Rusty Lake Paradise
Shared: Indie · Puzzle · Adventure

Chants of Sennaar
Shared: Adventure · Indie · Puzzle

Tomb Raider Game of the Year
Shared: Adventure · Action · Singleplayer

MiSide
Shared: Horror · Story Rich · Psychological Horror