Games like Birthday
Games like Birthday include Unpacking, Zup! S, Hidden Folks, Baba Is You, and A Little to the Left. We matched them by the tags players give Birthday on Steam (Casual, Puzzle, 2D, Cute, and Pixel Graphics): closest matches first, and among equally close ones the better-known games.

Unpacking
Shared: Casual · Cute · Puzzle

Zup! S
Shared: Casual · Puzzle · 2D

Hidden Folks
Shared: Casual · Puzzle · Hand-drawn

Baba Is You
Shared: Puzzle · Indie · Pixel Graphics

A Little to the Left
Shared: Puzzle · Casual · Cute

OneShot
Shared: Pixel Graphics · Cute · Puzzle

Carto
Shared: Puzzle · Cute · Indie

Is This Seat Taken?
Shared: Casual · Puzzle · Cute

Zup!
Shared: Casual · Puzzle · 2D

Sticky Business
Shared: Casual · Cute · Relaxing

Zup! 2
Shared: Casual · Puzzle · 2D

Gorogoa
Shared: Puzzle · Hand-drawn · Casual

Zup! F
Shared: Casual · Puzzle · 2D

FEZ
Shared: Puzzle · Pixel Graphics · Casual

Zup! X
Shared: Casual · Puzzle · 2D

Zup! 3
Shared: Casual · Puzzle · 2D

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

Zup! 5
Shared: Casual · Puzzle · 2D

Coloring Game
Shared: Casual · Pixel Graphics · Relaxing

Assemble with Care
Shared: Casual · Puzzle · Indie

Zup! 6
Shared: Casual · Puzzle · 2D

DAVE THE DIVER
Shared: Casual · Pixel Graphics · Relaxing

Zup! 8
Shared: Casual · Puzzle · 2D

Cat Goes Fishing
Shared: 2D · Cute · Casual