Games like Escape The Maze
Games like Escape The Maze include Portal 2, Murders on the Yangtze River, Rise of the Tomb Raider™, Tomb Raider Game of the Year, and Human Fall Flat. We matched them by the tags players give Escape The Maze on Steam (Action, Casual, Adventure, Puzzle, and Education): closest matches first, and among equally close ones the better-known games.

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

Murders on the Yangtze River
Shared: Adventure · Puzzle · Indie

Rise of the Tomb Raider™
Shared: Action · Adventure · Puzzle

Tomb Raider Game of the Year
Shared: Action · Adventure · Exploration

Human Fall Flat
Shared: Puzzle · Adventure · Action

Pikuniku
Shared: Casual · Adventure · Indie

Portal
Shared: Puzzle · Puzzle Platformer · Action

The Room
Shared: Puzzle · Adventure · Indie

Planet of Lana
Shared: Action · Puzzle Platformer · Puzzle

The Unfinished Swan
Shared: Adventure · Puzzle · Indie

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

FAR: Lone Sails
Shared: Adventure · Puzzle · Indie

A Story About My Uncle
Shared: Adventure · Indie · First-Person

Chants of Sennaar
Shared: Adventure · Puzzle · Indie

FEZ
Shared: Puzzle · Indie · Adventure

Outer Wilds
Shared: Adventure · Exploration · Puzzle

Moncage
Shared: Casual · Puzzle · Adventure

The Room 4: Old Sins
Shared: Puzzle · Adventure · Hidden Object

Slime Rancher
Shared: Adventure · Exploration · Casual

Bendy and the Dark Revival
Shared: Action · Adventure · Indie

Bugsnax
Shared: Adventure · Puzzle · First-Person

LIMBO
Shared: Puzzle · Indie · Puzzle Platformer

Deliver Us The Moon
Shared: Action · Adventure · Indie

Supraland
Shared: Adventure · Puzzle Platformer · Exploration