How about the American Civil War? Were those not two democracies?
IMO, yes. The studies author argued that the Confederacy had not actually achieved independence with succession, hence was excluded. I do not agree with that reasoning.
Country vs. country not country vs self.
It was a rebellion, not a war between countries. Besides, when Davis and his government initiated hostilities they had been appointed not elected.
I believe that the rebellion was crushed before they had any time to actually hold a real election. Form 1864-on there wasn't really much of a governemnt to speak of at all; everyone was just kind of looking out for their own.