Socialism is defined by these characteristics:
- Strong, reliable, universal social welfare: you'll never end up homeless or starve to death no matter how much you screw up in life
- public services are all paid by the State through taxes: this includes healthcare, education, retirement, and disability
- A steeply progressive income and corporate tax system that absorbs excess profits and incomes to redistribute to the rest of the economy/population
- State ownership (but professional management) of certain key, strategic industries like energy, defense, transportation etc. The state should however NOT be heavily incentivized to personally profit from these enterprises.
So no, China is not socialist, not even by a long shot.
And this is a huge however, it is not capitalist or rather "corporatist" as the US and UK are either.
Thanks to the super wise and totally not at all lobbyist driven Supreme Court decision of Citizens United, corporate America is not allowed to legally by a politician, up to and including the US President.
It's no secret to anyone paying attention at this point that billionaires own all the political power in the US in all but name and title.
In contrast, China's billionaires are all CCP members, so the interests of the corporate China and "main street" China have to be aligned since the same person wears both hats, and is directly impacted by the consequences of both roles.
So while both China and the US are oligarchies, at least the Chinese version is a proper oligarchy where the people in charge are actually real government officials and not corporate executives.