The Red Army did get rid of 'ranks' in a more superficial sense in that someone commanding a division would be called a 'division commander', rather than 'general' (Or whichever rank commands a division, I'm not sure). There was a broad push to do away, even if just superficially, with symbols of the old order (not just in the military) - this is why there were commanders instead of officers and commissars instead of ministers, for example.

So basically, no. They renamed (and often reorganised) the ranks and structures that existed. There were still definite chains of command once the Red Army was organised. I can't speak to the PLA or Albanian army, but I would imagine it would be a similar story.

Someone with more of a background in the Soviets could give you some info on why they did this. It's an interesting way of looking at the new regime after the Russian Revolution (in my opinion).

There was still a chain of command. The commander of a platoon would still take order from a commander of a company but removing ranks meant that the political leadership could shuffle people at will.

Superficially this was sold as a way of getting rid of the old order, but much more pragmatically, the Bolsheviks did this for political expedience. Running the army as a political institution means that you have to be able to remove or replace people based on their political sentiments rather than any sort of seniority or experience. For example, if for political reasons you wanted to give a Lieutenant command of a battalion, many people would take significant issue with that and there would be a morale impact. Especially amongst the Captains who were now reporting to a more 'junior' officer.

But if that same person doesn't have a rank then appointing them to one job or another rankles (no pun intended) many fewer feathers.

Clearly, as most armies that have tried this have discovered, once they actually engage in combat this system falls flat on its face.