>But obviously this isn't how China is now and even state-owned companies in China generally operate in a market and can be in competition with private companies and other state-owned companies.
"Compete's in a market" is irrelevant to socialism. Again, basic poli sci, socialism encompasses both free market and captured market. What makes it socialism is government ownership of the means of production, with redistribution to the general populace.
>There are state-owned companies in all Western countries, by the way.
Right, and which western "capitalist" society has state ownerhsip of 70%+ of the "private" companies that make up its economy? Correct, 0. Socialism has never required the state to own all business in a given economy anymore than capitalism has required 0 ownership.