That is one aspect of communist ideology and that is the most innocuous aspect of it. That is not the sum of communist ideology or even the primary aspect of communist ideology which is neither dead in the former Soviet Union, China or anywhere else. Therefor one can hardly say the legacy of its "defeat" belongs to anyone.
And now I have to make dinner.
Bon appetit.
As far as Christianity fares in formerly Communist countries, or even in China, there is no comparison with pre-1973.
You know where Communism,-- central planning, dialectical materialism, atheism, and what have you, -- are metastasizing? Three guesses. It ain't Central or Eastern Europe.