WoWDB

It says it's account wide.  I think that makes it fine for people who main pures (I'm one of them).

I suppose going dps as discipline priest should work as well. I usually do up to 70-80k as disc in 5 mans.

Holy burst might be better.

I'd guess the tanking and healing options will be available to anyone, and they would be able to complete it with high enough dps

So...how will Warlocks, Rogues, Hunters, and Mages get this? 

The same way anyone else will: Completing the challenge in a spec not suited for it.

It gives you the option to attempt a challenge even if your class lacks the relevant spec. (As a Warrior it gave me the option for the healer challenge). From what I understand, doing the tank challenge as a dps isn't too difficult.

How I got it on my hunter as a tanking challenge... And it's been done on a frost mage as well. Non trivial, but I think every class can potentially get it with some time investment.