Not really. The “exact definition” of communist would be public ownership. Claiming that this is the same as state ownership, I think, would be giving way too much credit to China, it would imply that their government is legitimately carrying out the will of the public.

Also, “state-owned enterprises”, in China’s case, refer to capitalist enterprises in which the government is a major stakeholder. They’re publicly traded, are generally still primarily privately owned, they have profit motive, etc. That doesn’t sound particularly communist to me. These same kinds of enterprises exist all over Europe and North America, and we don’t call those “socialist or communist in nature.”