Games like Amber City
Games like Amber City include Machinarium, Carto, GRIS, Pikuniku, and Scribblenauts Unlimited. We matched them by the tags players give Amber City on Steam (Casual, Puzzle, 2D, Adventure, and Cute): closest matches first, and among equally close ones the better-known games.

Machinarium
Shared: Puzzle · 2D · Hand-drawn

Carto
Shared: Puzzle · Cute · Adventure

GRIS
Shared: Adventure · Female Protagonist · Hand-drawn

Pikuniku
Shared: Casual · Puzzle · Adventure

Scribblenauts Unlimited
Shared: Casual · Puzzle · Adventure

Zup! S
Shared: Casual · Puzzle · 2D

Muse Dash
Shared: Cute · Casual · Female Protagonist

Plants vs. Zombies GOTY Edition
Shared: Casual · 2D · Strategy

Gorogoa
Shared: Puzzle · Casual · Hand-drawn

Laughing to Die
Shared: Casual · Puzzle · Adventure

Planet of Lana
Shared: Puzzle · Female Protagonist · Puzzle Platformer

Monument Valley
Shared: Puzzle · Casual · Adventure

Zup!
Shared: Casual · Puzzle · 2D

Zup! 2
Shared: Casual · Puzzle · 2D

Hidden Folks
Shared: Casual · Puzzle · Hand-drawn

Storyteller
Shared: Puzzle · 2D · Adventure

LIMBO
Shared: Puzzle · 2D · Puzzle Platformer

Florence
Shared: Casual · Adventure · Cute

Sanfu
Shared: Puzzle · 2D · Adventure

Zup! 3
Shared: Casual · Puzzle · 2D

Donut County
Shared: Casual · Puzzle · Cute

The Last Campfire
Shared: Puzzle · Adventure · Cute

Munin
Shared: Casual · Puzzle · Adventure

BEEP
Shared: 2D · Adventure · Puzzle