Games like Sombre
Games like Sombre include The Room, The Room 4: Old Sins, The Room Two, The House of Da Vinci, and Supraland. We matched them by the tags players give Sombre on Steam (Adventure, Casual, Puzzle, Point & Click, and Choose Your Own Adventure): closest matches first, and among equally close ones the better-known games.

The Room
Shared: Puzzle · Point & Click · Adventure

The Room 4: Old Sins
Shared: Puzzle · Adventure · Point & Click

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

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

Supraland
Shared: Adventure · Puzzle Platformer · Exploration

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

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

Morphopolis
Shared: Puzzle · Casual · Adventure

Boxes: Lost Fragments
Shared: Puzzle · Adventure · Point & Click

Portal 2
Shared: Puzzle · Puzzle Platformer · First-Person

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

Monument Valley
Shared: Adventure · Puzzle · Casual

Big Walk
Shared: Puzzle · Adventure · Exploration

VLADiK BRUTAL
Shared: Adventure · FPS · Casual

Moncage
Shared: Casual · Puzzle · Adventure

Gorogoa
Shared: Puzzle · Casual · Point & Click

Little Nightmares
Shared: Adventure · Puzzle · Puzzle Platformer

The Unfinished Swan
Shared: Adventure · Puzzle · Exploration

Frankenstein: Master of Death
Shared: Casual · Point & Click · Adventure

Viewfinder
Shared: Puzzle · Puzzle Platformer · Adventure

FEZ
Shared: Puzzle · Adventure · Casual

COCOON
Shared: Adventure · Puzzle · Exploration

Outer Wilds
Shared: Adventure · Exploration · Puzzle

Spirit of the North
Shared: Adventure · Puzzle · Casual