Consider this: Victorian England was the prototypical Capitalist economy, but the entire economy was not subject to the Capitalist mode of production. In parts of the empire, there were still peasants and feudal power structures; some parts of the economy were also government-owned.

What made Victorian England a Capitalist state is that the economy was predominantly Capitalist, and that the Capitalist Class was the one in charge.

In China, the majority of the economy is state-run. The state operates steel mills, mines, and farms (though many farms are also homesteads or cooperatives, from what I understand none are privately owned). Capitalists operate tech firms and consumer good factories.