It's a chance to beat someone up !
Why would you want to play chess boxing?

Interesting thought . When participants are involved in a game of Chess it's often said they are "playing". One almost never hears Boxers described as "playing" while boxing.
I like the idea of having to be proficient mentally as well as martially. A lot of people can't compete on both levels. Having said that, I prefer grappling or MMA to boxing.
Why would you want to play chess boxing?