As it's defined in the OP, no I don't care. Chinese movies and music is certainly less globally influential than, say, Indian movies and music, which has a lot more broad interest in the West.
But, I am interested in how Chinese people live their lives, what their political and social aspirations are, and other facets of life in China. It's just nothing more than a trivial, passing interest. I think China may interest me more than some other cultures just because of the radical transformations it's undergone in the last century. The prior 100 years of Chinese history have been both devastating and reformative, more so than any other large culture/country in the world... And there's something unique to that. China has been a sort of petri-dish of social engineering experiments over the last century, and I wish that I could see it from the perspective of a 500-year lens or something, instead of seeing a lot of this transformation contemporaneously.