Forgot to answer this one.
The ones on WAX have special meaning on WAX and the ones on HIVE the same thing for HIVE.
You are either able to play from either of the sides you get the "rules" to start playing accepted.
Although, the more NFTs you have on both sides, the more time you can play the game (like an allowance for the total number of NFTs). And in the future, you never know what could also be possible. Maybe they will be interchangeable (I don't know). For now, you either need to complete the rules of one of the sides to start playing, and then if you have extra NFS you get some bonus.
I have just won BOOM and DOOM today for example.