There was this book called The Communist Manifesto. The government of China doesn't look very much like the book. So, not communist.
But China is ruled by the Chinese Communist Party. So yes, communist, at least by their own declaration.
(You see this same thing in the US, where the Republicans and Democrats get the other side shoving in their face every statement made by every nutcase who manages to win a primary.)
I would say that the problem comes from them being a one-party dictatorship, with the explicit intention of never giving that up. That doesn't lead to a government that is accountable to the people; it's a government that is trying very hard to avoid being accountable to the people.
I would also say that Xi is making them more genuinely communist than they were 15 years ago.