You just said:

the Chinese civil war was not fought with ballots or debates, it was fought with guns, on both sides.

Ultimately, the people with the guns hold all political power in society.

That directly contradicts Mao's idea that guerillas are supported by the people they live with. If the people withhold support, guerillas become like a fish out of water. Ordinary people (without guns) actually exercise more power in this scenario.

By focusing on guns instead of class, you are not using a Marxist or Neo-Marxist framework to analyze the civil war. You are using a Realist or Neo-Realist framework, similar to Henry Kissinger. Marxist frameworks believe class is much more important than guns.

The statement "political power flows from the barrel of a gun" is almost anti-Marxist in the way it completely ignores class conflict.