It’s also not a variant of communism: first, in the Marxist-Leninist interpretation the purpose of the single party is expression of and progress towards the dictature of the proletariat, the single-party state is not communist (they claim socialism instead) and the ultimate goal is self-abolition (turns out all other issues aside it’s difficult to make such a system abolish itself).
Second, Libertarian Marxist as well as Trotskyists oppose the use of a transitional one-party state and “democratic centralism”.
That's not what happened in China.
The revolution in China was a _Communist_ one. Maoism is "Communism with Chinese characteristics". That's when 10s of millions of Chinese men, women and children were murdered to further the Communist utopia.
After Mao's death, Deng instituted many reforms and it would be arguable that it was no longer Communist -- but it would be rubbish to call it Capitalism. The government runs _everything_. Where they don't own corporations outright, they install party members to oversee them or own them "individually".
Look at what happened to Jack Ma to see exactly how NOT capitalist the country is.
Also I would not exclude that these companies can be put in their place by using already existing laws. No need for new laws, it's a matter of political will.
Who precisely do you think has 90% of the power in 90% of businesses? And before you say 'the shareholders, duh', the venn diagram of the PMC and shareholders of these massive corporations is a circle. The ruling class is the PMC. They run the corporations. How could it be any other way?
This last bit is the most important. Even if you don't want to blame the managers, profit and loss mechanism is gone, so we are not under capitalism but in a command economy
Communism is when all property is publicly owned and each person works and is paid according to their abilities and needs.
So pure communism precludes corporations that are owned by private individuals.
Some sort of capitalist-imperialism, maybe, but definitely not communism.