I am pretty sure China considers itself a "democracy" in the original meaning of the word: "rule of the people" (thus the focus on "People" in "People's Republic of China" and in many other official names). Basically, anyone can rise to power by going through the ranks of the communist party, and people are elected and voted for.
I wouldn't consider it a democracy even in that basic sense because of the disregard for basic human rights and freedoms, and it surely is not one in the modern political sense of multi-party systems.
Similarly, one could argue that the de-facto two-party system in the USA is not very democratic either, as it's not unlike a single-party system in China: you go through the ranks of the *party* to progress. It's the other things that make USA more of a democracy (freedom of speech and protections against unsubstantiated persecution, for example, and sure, ability to start a party too — even if it's inconsequential).