Well there is no "socially responsible" version of free markets. The market is either free, meaning free of undue and unnecessary interference by the government or it's not. That "socially responsible" is just an excuse for control.
And the non-businessmen's definition of "free market" is not in contrary to what a businessman's definition really, it's just one reflection of it. Withoutq government's interference, a free market is where there is free competition", or "a market where both buyer and seller are equally free to turn down a deal."
Again, you over simplify things, particularly when talking about China. There is an inherent love hate relationship between business and government in all countries.
Ideally, business wants no competition, no government oversight, low paid labor but a huge market that can afford its products. Business cares about nothing but bottom line.
Government is more complicated because there are various types. In democracies, government is elected by the people and meant to protect and further the interests of society as a whole against special interests, like business, military, clergy and foreign powers. In dictatorships, society is under the control of one or more of the special interest groups, sometimes simply to drain the resources of the state for their sole benefit, but also to set the direction for the nation, as in most populist dictatorships from the right and the left.
In China's case, you think it's an excuse for control but Chinese society in general wants their government to exercise that control. Ask the Chinese on the street and they would generally agree with their government's intervention in western China, to fight separatism and kill those who kill Han Chinese. To the common Han or Cantonese Chinese, Uyghur Chinese must learn to integrate and, if it means re-education camps? then reeducate. The nation as a whole is more important than the special interests of some.
The Chinese government projects itself as the righteous conscience of the nation with a stick. The citizens aren't duped but they prefer order to disorder and the government has significantly increased their standard of living.
China is still far from modern. For a communist country boasting paternalistic oversight, it still has no consumer mechanism to protect buyers from scammers. When harm is grievous, scammers are hung or spend 30 years in jail and that is supposed to scare others from doing the same and it works for about a month before things go back to the way things were. There is no impartial legal system because the judicial is government and scams frequently involve low level officials.
But China's incredible success is undeniable. In my opinion, it is because of the efficiency of central planning and it frightens Americans capitalists to the core, because in America nothing is planned, everything is left to negotiation between government, business, judiciary and various other special interest groups. Beside the anarchic consequence of this, everything takes very long to reach agreement, everything become very expensive and ultimately the result is not necessarily better than if the decision was made by central planning with only the greatest benefit in mind.
Europe is a good example of nations setting central planning agenda while also taking local considerations in the decision mix. The pace of development is faster than in the US where today little gets done and most everything is reactive.
