That having been said, Communism in China is dead. I've talked with party members on the subject, as well as students. 'Gongchan zhuyi' (literally 'public production- ism) is the tired old product that the government pushes because of habit and name recognition. The ideas behind it carry no water. In historical reference, it's as if the beauracrats are running the country for an Emperor who has no interest in the affairs of state. They use his name, and his seal, but he's nowhere to be found.
They can't refer to themselves as Nationalist, since that name is synonymous with the old government. They don't really have a choice but to keep the same name, since there is no dynasty to install, nor any new belief. Fascist is the most accurate term, but that word (faxi zhuyi) literally means 'Western method ism', and that wouldn't sit well with anyone.