They can't, and it's because of one simple reason, which PokeMMO state on their website:
* You must have the legal right to use that rom. We will not supply you with the roms, or help you find them as they are copyrighted
They dodge DMCA strikes because they require the user to provide the rom of the game, and their client just uses all that data
As long as they don't specifically provide something copyrighted in the Pokemon franchise, they're all good
As far as I know it's kind of a grey area, because you can use all the content you want as long as you don't publicly redistribute it, but you're not allowed to 'hack' your device, download or otherwise obtain the rom without official consent from Nintendo
I'm not a lawyer, so I don't know whether Nintendo can do anything about the name itself "PokeMMO", but I imagine not since they are not using the full name "Pokemon"
Someone correct me if I'm wrong