Yes. They're a state controlled capitalist society.
Their entire model is based around commodities, labor exploitation and controlling foreign debt. Their entire current economic system is using cheap labour to make export commodities, as well as infrastructure and debt generation in foreign countries. What do you think Belt and Road is if not the largest state-sponsored capitalist endeavor on the planet currently?
Just because they put "communist" in their title does not make them an anti-capitalist society. Just like DPRK is not democratic.
China's economic system is complicated.
It is (was) the world's sweatshop, but it is absolutely not a free market. The state itself owns or is able to arbitrarily take control of every business in the country. Competition isn't free and the state itself can pick the winners it wants. The country also has almost nothing in the way of IP protection, so foreign companies have to deal with a ton of bullshit and uneven competition. Companies that reach a certain size are required to have Communist Party members on the board to oversee their actions.
So in some ways they are not regulated (safety, IP, workers rights) but in other ways the state runs and manipulates the economy, which is very much against the spirit of Capitalism.
Honestly the only thing stopping the country from being labeled as classically Fascist is the relative lack of state-sponsored violence. Most of the other tenets are already there, with the ethno-nationalist angle being more of a background element for now.