Other opinions:
They are not communist. Communism does not have a centralized government. They are closer to socialism than communism. I would say a mixture of totalitarian and socialism.
China was never Communist, it was Socialist, but now it's basically a single party, part socialist, part capitalist, authoritarian/ totalitarian oligarchy with figurehead leaders.
Functionally, it is a highly bureaucratic, multi-level, single-party republic. Starting at the very lowest levels, the Chinese elect a representative to serve on a local council. These councils elect a representative to the city council, which elects a member to a regional council, etc. The current
system requires everyone to be a member of the same political party. The system can be called communist, however, it is a relatively unique system in which an established bureaucracy is interwoven into a republican structure with marxist overtones (philosophy). Frankly, it's a bit of puzzle to classify.
The People's Republic of China is a single-party republic. The only political party is the Communist Party so even though there are "elections" in China, they are all members of the same political party. And even then, the Chinese people have a lot less say in who their leaders are than in a western-style democracy or republic.
There is the concept of "One country, Two systems". Since the return of Hong Kong and Macau to China is 1997 and 1999 respectively, the Central government has granted the two special administrative regions some forms of political freedom, such as the democratic election of the Chief Executive in 2012 in Hong Kong.