I think you are oversimplifying the events. I'm not suggesting there was nothing wrong with EAM. However, the article is about the British involvement that lead to the December '44 events. They freed and armed the Greeks who collaborated with the Nazi regime and they disarmed (or tried to disarm) only ELAS members. Of course Greek citizens would protest against that. And it was policemen armed by the British who opened fire against a peaceful crowd. I really can't see how you can justify this.
You assume that all members of EAM/ELAS were communists. They were not. Also, there really was a window for them to take over: after the Nazis left and before the Allied forces arrived they were practically the only armed force in Greece. However they chose to wait.
Mark Mazower's "Inside Hitler's Greece: The Experience of Occupation 1941-44" is an excellent book on the subject.
So since some of the Greek fighters - meaning those who allied with the British against the Nazis, had communist ideals you assume that all they wanted was a violent take over and establishing communism. And based on that assumption you justify the British for (a) arming Nazi collaborators and (b) opening fire against civilians in a peaceful demonstration.