They aren't exactly capitalists but they definitely aren't communists. Funnily enough, their economic system is a lot more reminiscent of old school fascism. One of the often forgotten aspects of what fascism means is an economic and political system where the government controls the economy by mandating the power of a few certain large corporations (that the government selects, and can un-select at any time), but another aspect of fascism is that the government rarely if ever wants to get rid of one of these corporations of take away any of their power because corruption and fasicm go hand in hand - the government props up a few corporations and gives them practically unlimited power over their industries because they get paid by those companies, and so the system reinforces itself.
Wouldn't you say that that's a fair description of how China works? Also to be clear I'm not at all talking about any part of fascism other than the economic aspect of it (like how you can talk about capitalism without talking about the entire political structure of a country - just the economics..)
(also most people who use the world fascism more often just mean "totalitarian". Fascism is one of several different totalitarian systems, and the things that people usually associate with fascism are just the totalitarian aspect of it. There is more to what it means, it is a specific type of totalitarianism - like how state communism is another specific type of totalitarian system. I.E. they both include things like suppressing freedom, eliminating political opponents, killing free speech. etc - but the economies are different)