Why can't Jehovah's Witness play chess?

It is not a general rule not to play any particular game. Each individual has to make their own informed decision about what God requires of them. Each person train their conscience different and their choices sometimes differs, with time, they can even decide differently, and no one - not any witness will judge the other - as Jehovah is the supreme judge. However, witnesses engage in what is spiritually upbuilding, and refressing. e.g a bible-based game produced by www.TheocraticGames.com is such a spiritually upbuilding game. We remember each one of them will give account to God alone.