Literally for at least 100 years the word "socialism" has been used to mean the process of transition from capitalism to communism guided by a communist party.
China is a socialist country because it meets that definition.
It is authoritarian because it is a state. All states are authoritarian, by definition.
It is state capitalist because that's what happens when a state guides a transition to communism within a capitalist world order.
And it's called the Communist Party of China, not the Chinese Communist Party, because it is named in the tradition of all Communist Parties - CPUSA (Communist Party of the USA), PCC (Party Communista de Cuba), CPV (Communist Party of Vietnam), etc