Like I mentioned before, Death Knight's can heal themselves. The process the players used was likely a constant tank rotation in order for the injured ones to heal themselves up using Death Strike, Blood Pact, and Rune Tap, while the DPS just kept themselves alive through similar processes. This is why it took so long for them to take him down, as they had to make sure to keep moving him as much as possible and it would only take one screw-up for the whole thing to fall apart. Ragnaros himself is very heavy in location damage that can be avoided, so if they planned it correctly, they wouldn't have to heal often.Druids/Paladins could obviously do it, they each have a healer spec. Druids also have a ranged spec. Death Knights do not have either.
It is one hell of an achievement, but it would not be possible if they didn't have methods to heal themselves, which I mentioned before is the only reason you see them as "overpowered". The healing factor of the class has always been the lynch pin, and if used correctly, can be abused, but would take lots of effort. You know back in WOTLK before 3.3, a rogue soloed Grobbulus? These types of things can happen if someone puts their mind to it and knows their class extremely well.
Again, a DK in a general game setting, as in, grouped with other classes, is not overpowered compared to the other classes he is taking part. That is the crux of it as I thought I explained. If we can argue that DKs are overpowered because of the tools they have allowing them to single-class a boss, then I can argue that Druids and Paladins are just as overpowered. DKs are healers, they just can only heal themselves.