The term 'anime' itself is derived from the Japanese loanword for animation, so it's likely Chinese animation called something else. For China to have an equivalent, it would require a lot of developments in limited animation (i.e. reuse of stock frames, reduced frame rate, etc.), as well as influences brought over from the United States (i.e. comics, Disney cartoons). Unfortunately, the environment just isn't there for it. Between a long period of civil war, anti-Western feelings and rabid censorship to preserve either tradition (in Taiwan) or revolutionary ideology (in China), comic artists for mature themes are few and far between, AFAIK.
Have a China more open and accepting of Western animation and comic styles would help a great deal, just as long as it doesn't get infected by Saturday Morning Cartoon syndrome.