...by your description basically every industrializing nation with heavy protectionism or state-sponsored company charters would be socialist. Was the East India Company a socialist endeavor? State ownership and interference has little to do with socialism proper and more to do with protection. State ownership exists in many economies, from fascism, corporatism, and feudalism to capitalism.
"Therefore, we repeat, state ownership and control is not necessarily Socialism – if it were, then the Army, the Navy, the Police, the Judges, the Gaolers, the Informers, and the Hangmen, all would all be Socialist functionaries, as they are State officials – but the ownership by the State of all the land and materials for labour, combined with the co-operative control by the workers of such land and materials, would be Socialism."
"But of late, since Bismarck went in for State-ownership of industrial establishments, a kind of spurious Socialism has arisen, degenerating, now and again, into something of flunkyism, that without more ado declares all State-ownership, even of the Bismarkian sort, to be socialistic. Certainly, if the taking over by the State of the tobacco industry is socialistic, then Napoleon and Metternich must be numbered among the founders of Socialism."
China's current economy is not in any way, shape, or form a socialist economy other than on paper, described through a lens of state ownership justified as socialist state-capitalist economic evolution.
It would be the equivalent of me trying to argue the US is in fact feudalist, because local lords (business owners) own land that I must work, with them getting the spoils and in return they grant me some benefits and protections. These lords owe allegiance to other lords (parent companies) and their families (shareholders) and interact in alliances and power struggles (market competition). I mean, you can make any ideology and economy superficially fit any description with enough cherry picking and manipulation. Stalin argued that social democracy was a variant of fascism. Hitler argued there were notable similarities between western capitalism and Soviet socialism.
China maintains the socialist label so as to not lose legitimacy as the continuation of the communist government established in 1949. If they simply give up the communist aesthetic, they're no different than any protectionist corporatist regime plucked right out of early 20th century Europe. There are, of course, many breaks in the ideological line of socialism and communism that would disqualify them from being accurately described as socialist or communist, but it's convenient both for them and their detractors to suppose themselves communists and socialists when in fact China is engaging in a massive protectionist state-directed capitalist experiment for the purpose of private ownership and private gain. Replace the hammer and sickle with a dystopian megacorp logo from the 80s and there's practically no distinction between Chinese "socialism" and the hypercapitalist state.