Games like HyperRogue
Games like HyperRogue include Manifold Garden, Antichamber, Hylics, Moncage, and Lucid Blocks. We matched them by the tags players give HyperRogue on Steam (Turn-Based Tactics, Psychedelic, Experimental, Hex Grid, and Surreal): closest matches first, and among equally close ones the better-known games.

Manifold Garden
Shared: Surreal · Psychedelic · Experimental

Antichamber
Shared: Surreal · Puzzle · Exploration

Hylics
Shared: Psychedelic · Surreal · Abstract

Moncage
Shared: Surreal · Puzzle · Experimental

Lucid Blocks
Shared: Psychedelic · Surreal · Open World

Hyperbolica
Shared: Surreal · Psychedelic · Exploration

Into the Breach
Shared: Turn-Based Tactics · Turn-Based Strategy · Puzzle

Mewgenics
Shared: Turn-Based Tactics · Turn-Based Combat · Turn-Based Strategy

The Witness
Shared: Open World · Exploration · Puzzle

Superliminal
Shared: Surreal · Psychedelic · Puzzle

Fractal Block World
Shared: Surreal · Open World · Psychedelic

NaissanceE
Shared: Exploration · Surreal · Abstract

INDIKA
Shared: Surreal · Psychedelic · Puzzle

STAR WARS Zero Company™
Shared: Turn-Based Tactics · Turn-Based Strategy · Turn-Based Combat

Urtuk: The Desolation
Shared: Turn-Based Tactics · Hex Grid · Procedural Generation

Disillusion
Shared: Experimental · Psychedelic · Abstract

Viewfinder
Shared: Surreal · Puzzle · Abstract

Tactical Breach Wizards
Shared: Turn-Based Tactics · Puzzle · Turn-Based Strategy

Monster Sanctuary
Shared: Turn-Based Tactics · Exploration · Turn-Based Combat

江湖十一
Shared: Open World · Turn-Based Tactics · Exploration

Warhammer 40,000: Mechanicus
Shared: Turn-Based Tactics · Turn-Based Combat · Strategy

Fell Seal: Arbiter's Mark
Shared: Turn-Based Tactics · Turn-Based Combat · Indie

The Last Spell
Shared: Turn-Based Tactics · Turn-Based Strategy · Turn-Based Combat

Obduction
Shared: Exploration · Puzzle · Surreal