Games like Twelve Minutes
Games like Twelve Minutes include Outer Wilds, The Room, The Room Three, Sally Face - Episode One, and Chants of Sennaar. We matched them by the tags players give Twelve Minutes on Steam (Indie, Adventure, Mystery, Puzzle, and Story Rich): closest matches first, and among equally close ones the better-known games.

Outer Wilds
Shared: Mystery · Adventure · Story Rich

The Room
Shared: Mystery · Puzzle · Adventure

The Room Three
Shared: Adventure · Mystery · Puzzle

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

Chants of Sennaar
Shared: Adventure · Indie · Puzzle

Firewatch
Shared: Adventure · Mystery · Story Rich

Return of the Obra Dinn
Shared: Mystery · Puzzle · Indie

The Room 4: Old Sins
Shared: Mystery · Puzzle · Adventure

The Room Two
Shared: Mystery · Puzzle · Adventure

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

Servant of the Lake
Shared: Adventure · Puzzle · Indie

Rusty Lake Paradise
Shared: Indie · Puzzle · Adventure

The Sexy Brutale
Shared: Mystery · Puzzle · Adventure

The White Door
Shared: Indie · Adventure · Puzzle

Blue Prince
Shared: Mystery · Puzzle · Indie

The Rewinder
Shared: Adventure · Mystery · Puzzle

The House of Da Vinci
Shared: Mystery · Puzzle · Adventure

Unheard - Voices of Crime
Shared: Mystery · Puzzle · Indie

Fran Bow
Shared: Puzzle · Story Rich · Adventure

Sherlock Holmes: The Devil's Daughter
Shared: Adventure · Mystery · Story Rich

OneShot
Shared: Indie · Story Rich · Puzzle

Gorogoa
Shared: Indie · Puzzle · Singleplayer

Samsara Room
Shared: Indie · Adventure · Puzzle

There Is No Game: Wrong Dimension
Shared: Indie · Adventure · Puzzle