Games like Black Mirror III
Games like Black Mirror III include The Room 4: Old Sins, The Room, The Room Two, The Room Three, and Servant of the Lake. We matched them by the tags players give Black Mirror III on Steam (Adventure, Point & Click, Horror, Puzzle, and Mystery): closest matches first, and among equally close ones the better-known games.

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

The Room
Shared: Point & Click · Puzzle · Mystery

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

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

Servant of the Lake
Shared: Adventure · Point & Click · Puzzle

Cube Escape Collection
Shared: Point & Click · Puzzle · Horror

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

Rusty Lake Paradise
Shared: Point & Click · Adventure · Puzzle

Underground Blossom
Shared: Adventure · Point & Click · Puzzle

Little Nightmares
Shared: Adventure · Horror · Puzzle

Fran Bow
Shared: Point & Click · Adventure · Puzzle

Little Nightmares II
Shared: Adventure · Horror · Puzzle

Outer Wilds
Shared: Adventure · Mystery · Story Rich

Samsara Room
Shared: Adventure · Puzzle · Point & Click

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

Firewatch
Shared: Adventure · Story Rich · Mystery

The Walking Dead
Shared: Adventure · Point & Click · Story Rich

Syberia 3
Shared: Adventure · Point & Click · Puzzle

Murdered: Soul Suspect
Shared: Adventure · Horror · Mystery

The Rewinder
Shared: Adventure · Mystery · Puzzle

Stray
Shared: Adventure · Singleplayer · Atmospheric

Black Mirror
Shared: Adventure · Point & Click · Horror

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

Sherlock Holmes: Crimes and Punishments
Shared: Adventure · Mystery · Puzzle