Games like Believe
Games like Believe include The Room, The Room Three, Papers, Please, The Room 4: Old Sins, and Boxes: Lost Fragments. We matched them by the tags players give Believe on Steam (FPS, Education, Puzzle, Point & Click, and 3D): closest matches first, and among equally close ones the better-known games.

The Room
Shared: Puzzle · Point & Click · Atmospheric

The Room Three
Shared: Puzzle · Point & Click · Atmospheric

Papers, Please
Shared: Point & Click · Puzzle · Multiple Endings

The Room 4: Old Sins
Shared: Puzzle · Point & Click · First-Person

Boxes: Lost Fragments
Shared: Puzzle · Point & Click · 3D

The House of Da Vinci
Shared: Puzzle · Point & Click · 3D

The Room Two
Shared: Puzzle · Point & Click · Atmospheric

Return of the Obra Dinn
Shared: Puzzle · First-Person · Atmospheric

Battlefield™ 1
Shared: FPS · First-Person · Historical

Portal 2
Shared: Puzzle · First-Person · Singleplayer

Gorogoa
Shared: Puzzle · Point & Click · Casual

Mirror 2: Project X
Shared: 3D · FPS · Multiple Endings

Chants of Sennaar
Shared: Puzzle · Point & Click · Singleplayer

VLADiK BRUTAL
Shared: FPS · First-Person · Puzzle

Myst
Shared: Puzzle · First-Person · Point & Click

Liars Bar
Shared: FPS · Casual · 3D

There Is No Game: Wrong Dimension
Shared: Puzzle · Point & Click · Indie

Riven
Shared: Puzzle · First-Person · 3D

The Talos Principle
Shared: Puzzle · First-Person · Atmospheric

Half-Life 2
Shared: FPS · First-Person · Singleplayer

Moncage
Shared: Puzzle · Casual · Singleplayer

Black Mesa
Shared: FPS · First-Person · Singleplayer

SUPERHOT
Shared: FPS · Puzzle · First-Person

PC Building Simulator
Shared: Education · First-Person · 3D