China is Socialist. The overall system is Socialism with Chinese Characteristics, categorised as a largely Market-based economy carefully pruned, planned, and controlled by the government. The state ideology is Marxism-Leninism, and Xi Jinping Thought.

The notion that China must be Capitalist because it has markets could be applied to say the US is Socialist because it has a State-Run Post Office. What's important is the class that retains power.

In the US, private banks, large businesses, and exceedingly wealthy individuals direct the state. The state is run in their interests, and this guides policy more than anything.

In the PRC, the Proletariat is in control via the CPC. Capitalists are firmly kept in check and dealt with if they step out of line, there are large public infrastructure projects, real wages for the Proletariat are rising, and there aren't large privitization projects.

If you don't have a strong understanding of Marxism, it's easy to misanalyze whether or not a system is Socialist.