I really don't think much about Civil Wars, so I pulled this from Wikipedia:

"A civil war is a war between organized groups within a single nation state[1], or, less commonly, between two nations created from a formerly-united nation state[2]"

Given this, I stand by my position that the Eglish example was an insurgency, as one player was the state, correct?

So if it breaks into two states, and they fight: Civil War
If two organized groups within the state fight each other: Civil War
If an organized group fights the sitting power to either change it, break away from it, or remove it as in iligitimate outsider: Insurgency.

Mr. Webster may differ, but that's how I see it.