Games like Move That Box
Games like Move That Box include Baba Is You, There Is No Game: Wrong Dimension, Patrick's Parabox, Strange Jigsaws, and LYNE. We matched them by the tags players give Move That Box on Steam (Puzzle, Adventure, Logic, Sokoban, and Minimalist): closest matches first, and among equally close ones the better-known games.

Baba Is You
Shared: Puzzle · Logic · Indie

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

Patrick's Parabox
Shared: Puzzle · Logic · Sokoban

Strange Jigsaws
Shared: Adventure · Puzzle · Casual

LYNE
Shared: Puzzle · Logic · Minimalist

Zup! S
Shared: Puzzle · Casual · Indie

FEZ
Shared: Puzzle · Pixel Graphics · Adventure

Hexcells
Shared: Puzzle · Logic · Casual

Minit
Shared: Adventure · Puzzle · Minimalist

Void Stranger
Shared: Puzzle · Sokoban · Adventure

Hexcells Infinite
Shared: Puzzle · Logic · Casual

I hate this game
Shared: Puzzle · Logic · Pixel Graphics

OneShot
Shared: Pixel Graphics · Puzzle · Indie

LIMBO
Shared: Puzzle · Adventure · Indie

Out There Somewhere
Shared: Puzzle · Adventure · Pixel Graphics

Pikuniku
Shared: Adventure · Puzzle · Indie

Hook
Shared: Puzzle · Casual · Minimalist

UFO 50
Shared: Pixel Graphics · Indie · Adventure

Paquerette Down the Bunburrows
Shared: Logic · Puzzle · Sokoban

Zup! 2
Shared: Puzzle · Casual · Indie

Thimbleweed Park™
Shared: Adventure · Puzzle · Pixel Graphics

Dude, Stop
Shared: Puzzle · Pixel Graphics · Adventure

The Rewinder
Shared: Adventure · Puzzle · Pixel Graphics

McPixel
Shared: Puzzle · Adventure · Pixel Graphics