Chess: one of the most popular iOS apps also happens to have an Apple Watch interface. You will be able to challenge friends, solve puzzles, and view lessons.
Checkers for Apple Watch: chess not your cup of tea? This app lets you play checkers on your wrist.
Watch Chess: provides you with real time games from top chess tournaments. You get push notifications when rounds begin and end. The app has an Apple Watch interface too.
Have you found better board games for Apple Watch? Please share them here.