Games like Reversi
Games like Reversi include Bloons TD 6, Richman 11, UNO, Richman10, and Rento Fortune: Online Dice Board Game (大富翁). We matched them by the tags players give Reversi on Steam (Casual, Strategy, Board Game, Turn-Based Tactics, and 2D): closest matches first, and among equally close ones the better-known games.

Bloons TD 6
Shared: Strategy · Casual · Multiplayer

Richman 11
Shared: Casual · Board Game · Turn-Based Tactics

UNO
Shared: Casual · Board Game · Strategy

Richman10
Shared: Casual · Strategy · Board Game

Rento Fortune: Online Dice Board Game (大富翁)
Shared: Casual · Board Game · Strategy

Plague Inc: Evolved
Shared: Strategy · Casual · Multiplayer

No Time to Relax
Shared: Board Game · Casual · Strategy

100% Orange Juice
Shared: Board Game · Strategy · Casual

ShellShock Live
Shared: Strategy · 2D · Casual

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

Clue/Cluedo: Classic Edition
Shared: Board Game · Strategy · Casual

Chess Ultra
Shared: Strategy · Board Game · Casual

Blood Bowl 2: Legendary Edition (Classic)
Shared: Strategy · Board Game · Multiplayer

Liars Bar
Shared: Casual · Multiplayer · PvP

Hasbro's BATTLESHIP
Shared: Board Game · Strategy · Casual

Carcassonne - Tiles and Tactics
Shared: Strategy · Board Game · Casual

Stick Fight: The Game
Shared: Multiplayer · Casual · 2D

Blood Bowl 3
Shared: Strategy · PvP · Board Game

Swords and Sandals Classic Collection
Shared: Strategy · Casual · Board Game

Golf With Your Friends
Shared: Casual · Multiplayer · Strategy

5D Chess With Multiverse Time Travel
Shared: Board Game · Strategy · Chess

Wingspan
Shared: Board Game · Strategy · Casual

Chess
Shared: Casual · Board Game · Turn-Based Tactics

Talisman: Digital Classic Edition
Shared: Board Game · Strategy · Multiplayer