Games like The Cat and the Box
Games like The Cat and the Box include Firewatch, What Remains of Edith Finch, The Beginner's Guide, MiSide, and Return of the Obra Dinn. We matched them by the tags players give The Cat and the Box on Steam (Indie, Story Rich, First-Person, Atmospheric, and Singleplayer): closest matches first, and among equally close ones the better-known games.

Firewatch
Shared: Story Rich · Atmospheric · First-Person

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

The Beginner's Guide
Shared: Story Rich · Indie · Atmospheric

MiSide
Shared: Story Rich · First-Person · Singleplayer

Return of the Obra Dinn
Shared: Story Rich · Indie · Atmospheric

A Story About My Uncle
Shared: First-Person · Indie · Singleplayer

No, I'm not a Human
Shared: Indie · Story Rich · Singleplayer

The Talos Principle
Shared: First-Person · Story Rich · Atmospheric

OneShot
Shared: Story Rich · Indie · Atmospheric

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

Gone Home
Shared: Indie · Atmospheric · First-Person

METRO 2033 Redux
Shared: Story Rich · Atmospheric · First-Person

Cyberpunk 2077
Shared: Story Rich · Singleplayer · First-Person

Metro Exodus
Shared: Story Rich · Singleplayer · Atmospheric

Mouthwashing
Shared: Story Rich · Indie · Atmospheric

Black Mesa
Shared: First-Person · Singleplayer · Atmospheric

BioShock Infinite
Shared: First-Person · Story Rich · Singleplayer

BioShock™ Remastered
Shared: Story Rich · Atmospheric · First-Person

Outer Wilds
Shared: Story Rich · Atmospheric · Indie

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

Road 96
Shared: First-Person · Story Rich · Atmospheric

INSIDE
Shared: Atmospheric · Story Rich · Indie

Bendy and the Ink Machine
Shared: First-Person · Singleplayer · Indie

Fallout 4
Shared: Singleplayer · Atmospheric · First-Person