Games like Enypnion
Games like Enypnion include Gorogoa, Machinarium, GRIS, There Is No Game: Wrong Dimension, and The Room. We matched them by the tags players give Enypnion on Steam (Adventure, Indie, Casual, Point & Click, and Puzzle): closest matches first, and among equally close ones the better-known games.

Gorogoa
Shared: Indie · Puzzle · Casual

Machinarium
Shared: Point & Click · Puzzle · Adventure

GRIS
Shared: Indie · Adventure · Atmospheric

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

The Room
Shared: Puzzle · Point & Click · Adventure

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

Samsara Room
Shared: Indie · Adventure · Puzzle

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

Chants of Sennaar
Shared: Adventure · Indie · Puzzle

LIMBO
Shared: Indie · Puzzle · Adventure

The White Door
Shared: Adventure · Indie · Point & Click

Fran Bow
Shared: Point & Click · Adventure · Puzzle

LUNA The Shadow Dust
Shared: Adventure · Indie · Casual

Storyteller
Shared: Point & Click · Adventure · Puzzle

Lost in Play
Shared: Point & Click · Puzzle · Surreal

Moncage
Shared: Indie · Casual · Adventure

Brothers - A Tale of Two Sons
Shared: Adventure · Indie · Atmospheric

Old Man's Journey
Shared: Adventure · Casual · Indie

Sally Face - Episode One
Shared: Indie · Adventure · Puzzle

Rusty Lake Hotel
Shared: Indie · Adventure · Point & Click

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

Papers, Please
Shared: Indie · Point & Click · Puzzle

The Room Three
Shared: Adventure · Puzzle · Indie

Hidden Folks
Shared: Casual · Indie · Puzzle