Games like The Dungeon Rules
Games like The Dungeon Rules include Slay the Spire, Inscryption, Slay the Spire 2, Vampire Crawlers: The Turbo Wildcard from Vampire Survivors, and Balatro. We matched them by the tags players give The Dungeon Rules on Steam (Card Battler, Sokoban, Casual, Dungeon Crawler, and Puzzle): closest matches first, and among equally close ones the better-known games.

Slay the Spire
Shared: Card Battler · Card Game · Deckbuilding

Inscryption
Shared: Card Battler · Card Game · Puzzle

Slay the Spire 2
Shared: Card Game · Card Battler · Deckbuilding

Vampire Crawlers: The Turbo Wildcard from Vampire Survivors
Shared: Card Battler · Dungeon Crawler · Card Game

Balatro
Shared: Card Game · Deckbuilding · Casual

Baba Is You
Shared: Puzzle · Sokoban · 2D

Ratropolis
Shared: Card Battler · 2D · Card Game

Patrick's Parabox
Shared: Sokoban · Puzzle · Casual

Die in the Dungeon
Shared: Card Battler · Card Game · Dungeon Crawler

Dice & Fold
Shared: Card Battler · Dungeon Crawler · Turn-Based Combat

SteamWorld Quest: Hand of Gilgamech
Shared: Card Battler · Card Game · 2D

Linelith
Shared: Casual · Puzzle · Sokoban

Yu-Gi-Oh! Legacy of the Duelist
Shared: Card Battler · Card Game · Deckbuilding

Zup! S
Shared: Casual · Puzzle · 2D

Breachway
Shared: Card Battler · Card Game · Deckbuilding

GWENT: Rogue Mage (Single-Player Expansion)
Shared: Card Game · Card Battler · Puzzle

Stacklands
Shared: Card Battler · Card Game · 2D

Monster Train
Shared: Card Battler · Card Game · Deckbuilding

Griftlands
Shared: Card Battler · Card Game · Deckbuilding

Animation Throwdown: The Quest for Cards
Shared: Card Battler · Card Game · 2D

Library Of Ruina
Shared: Card Game · Turn-Based Combat · Deckbuilding

9 Kings
Shared: Card Game · Card Battler · Deckbuilding

Decktamer
Shared: Card Battler · Card Game · Turn-Based Combat