Games like The Puppet Master
Games like The Puppet Master include Samsara Room, Poppy Playtime, We Were Here, The Mr. Rabbit Magic Show, and Varenje. We matched them by the tags players give The Puppet Master on Steam (Free to Play, Indie, and Puzzle): closest matches first, and among equally close ones the better-known games.

Samsara Room
Shared: Indie · Puzzle · Free to Play

Poppy Playtime
Shared: Free to Play · Puzzle · Indie

We Were Here
Shared: Free to Play · Puzzle · Indie

The Mr. Rabbit Magic Show
Shared: Puzzle · Free to Play · Indie

Varenje
Shared: Free to Play · Indie · Puzzle

Travellin Cats in Paris
Shared: Free to Play · Puzzle · Indie

Awkward Dimensions Redux
Shared: Free to Play · Indie · Puzzle

Path of Exile
Shared: Free to Play · Indie · Free To Play

Pixel Puzzles: Japan
Shared: Puzzle · Indie · Free to Play

Fingerbones
Shared: Free to Play · Indie · Puzzle

Idle Champions of the Forgotten Realms
Shared: Free to Play · Indie · Puzzle

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

Firework
Shared: Indie · Puzzle

LIMBO
Shared: Indie · Puzzle

TBH: Task Bar Hero
Shared: Free to Play · Indie · Free To Play

Ultimate Custom Night
Shared: Free to Play · Indie · Free To Play

SMITE®
Shared: Free to Play · Indie · Free To Play

Baba Is You
Shared: Indie · Puzzle

Coloring Game
Shared: Free to Play · Indie · Puzzle

Transformice
Shared: Free to Play · Indie · Free To Play

Banana
Shared: Free to Play · Indie · Free To Play

Chants of Sennaar
Shared: Puzzle · Indie

Aimlabs
Shared: Free to Play · Indie · Free To Play

RYB
Shared: Indie · Puzzle · Free to Play