I think it is missing only that one element. I think the people fighting are fighting for vengeance, not for ruling power. At least most of them are...Henry Kissinger calls it a civil war.
Its got all the elements of a civil war. The dictionary defintion fits. The level of violence fits. Just like Lebanon and Bosnia did.
I don't know why people are afraid to call a duck a duck. Most people in the world see it for what it is, and call it a civil war. I can see no reason to run away from calling it, what it is.
Bush fans have spent this whole war trying to redefine words. First, it wasn't an insurgency - it was just a few dead enders. Now, its not a civil war, its sectarian violence.
It doesn't make it any less chaos, just harder to end if all they want to do is wreak vengeance.