Games like Red's Kingdom
Games like Red's Kingdom include Portal 2, INSIDE, Pikuniku, LIMBO, and Little Nightmares. We matched them by the tags players give Red's Kingdom on Steam (Puzzle Platformer, Puzzle, Platformer, Cute, and Indie): closest matches first, and among equally close ones the better-known games.

Portal 2
Shared: Puzzle · Platformer · Puzzle Platformer

INSIDE
Shared: Puzzle Platformer · 2.5D · Indie

Pikuniku
Shared: Puzzle · Indie · Cute

LIMBO
Shared: Puzzle Platformer · Puzzle · Platformer

Little Nightmares
Shared: Puzzle Platformer · Puzzle · Indie

FEZ
Shared: Puzzle · Platformer · Indie

Trine 2: Complete Story
Shared: Puzzle Platformer · Platformer · Puzzle

The Last Campfire
Shared: Puzzle · Cute · Indie

Never Alone (Kisima Ingitchuna)
Shared: Platformer · Indie · Puzzle

Seen
Shared: Indie · Puzzle · Platformer

Toki Tori
Shared: Puzzle · Platformer · Indie

Planet of Lana
Shared: Puzzle Platformer · Puzzle · Platformer

Webbed
Shared: Cute · Puzzle Platformer · Platformer

Defy Gravity Extended
Shared: Puzzle Platformer · Platformer · Puzzle

Unravel
Shared: Puzzle · Platformer · Puzzle Platformer

Unpacking
Shared: Cute · Puzzle · Casual

Nihilumbra
Shared: Platformer · Puzzle · Indie

FAR: Lone Sails
Shared: Puzzle · 2.5D · Indie

Moss VR
Shared: Puzzle · Puzzle Platformer · Story Rich

Ori and the Will of the Wisps
Shared: Platformer · Cute · Story Rich

Donut County
Shared: Puzzle · Indie · Cute

CATO: Buttered Cat
Shared: Puzzle Platformer · Cute · Puzzle

LEGO® Builder's Journey
Shared: Cute · Indie · Puzzle

ibb & obb
Shared: Puzzle · Platformer · Indie