It's the empire fighting rebels. I just realized. It's not really a civil war. Ulfric is fighting the empire. It's a rebellion, not really a civil war.
This is wrong. Haven't read the entire thread yet, but I assume it's been explained "why" already. If it has not:
Skyrim is not a seperate nation fighting for independence, it is part of a larger empire, and has always been since the very beginning. It wasn't a province that was dominated, like Blackmarsh or Elsweyr, it was where the Empire was
born. Skyrim is as Imperial as the Imperial province, itself. The Stormcloak Rebellion
is a rebellion, true, but it is also a civil war.