Very interesting article. But this raises an interesting question.

The third principal condition, authority, is just as important. The point of the violence must be sovereign rule: combatants must be trying either to seize national power or to maintain it. This is the difference between, for example, the Russian civil war and the tribal rebellions now taking place in 14 of India's 28 states, or the late 1990s insurgency of Subcomandante Marcos in Mexico. Revenge, struggles for rights, mass criminality and positioning for economic gain are not sufficient, individually or severally. The opponents must be fighting to rule.
If a region wishes to seceede does that make it a civil war or not? Author considers ACW as a civil war because of it. Yet he doesn't seem to consider wars in Yugoslavia as such even though they were fought over same principle (and Bosnia was even more complicated as Bosnia wanted to seceed from Yugoslavia and Serb parts wanted to seceed from Bosnia). Ditto for Chechen war.

Also according to this you could call Korean war civil war as it was fought between Koreans in Korea (though divided in two states). It was the question of national authority (will ROK be part of DPRK and ruled from there or not).