Sure, there may be people who are interested in things Chinese, but will that interest translate to a signfificant degree of, to give it a label, soft power? Will China ever shape the world because of its cultural appeal, like the West has? (And of course, you could argue that although someone from, say, Singapore watches Friends or Star Trek on TV, it doesn't make them any more "Western") I mean, I've studied Qigong, read Lu Xun, Confucius, Gao Xingjian, Ma Jian, studied Chinese, read a lot of history, rummaged for films by Zhang Yimou, and so on and so forth. I've even got a Chinese painting hanging on my wall. But I'm not certain other Western people who aren't, for example, interested in travelling to or working in China, or what have you, would take up such cultural offerings with the type of gusto that would translate to what we might call a significant impact. The other gentleman (I assume he's male) asked whether coming out on top hinges solely on economics. I think that's a good question. I would argue that it's much more than that, but it's a very complicated issue.
Well, in the full sense of the word, soft power really means the ability to influence laws and policies of other states, not necessarily culture or entertainment. In that venue, China is more than capable of doing that. Any nation could for that matter.
As for culture appeal, like I said, it's pretty hard to say. American social influence in that aspect was a large part due to the technological advances (especially media) and it's people being from many places (like immigration) as well as being spread out to many places (like its overseas military). Western influence from Europe was largely due to colonialism of the past. The Europeans took several generations to achieved that level of dominance, you could say. The Americans sort of inherited that position and took it to another notch, one could say.
This is just my opinion. If let's say China wanted to do it like America, that is to reach the world but do it in a short time period, either it becomes more cosmopolitan and it's institutions spread out more, along with inheriting some of the roles the US does for the world. China is only doing that within a limited version, and for so many reasons probably can not afford to do more. So, I don't really see China being able to influence the world in the same way as the US.
However, it might, and emphasize might, be able to do it like the Europeans. That is that Chinese nationals and their many cultural institutions and practices are also spread out throughout the world, except it will take several generations to reach very deep within other nations' psyche. Instead of colonialism, just the sheer size of the numbers moving, working and interacting with one another throughout the globe would be sufficient enough for such effects. Along with steady birth rates and intermarriages can help. I know that part is somewhat controversial but it does have some truths in it.
Although this version of world influence is probably more realistic than the American version, I still have a hard time thinking it will come to be. Mainly because that many regions and countries are more organized than before and culture in many areas is a product of the environment. These are my opinions for the time being.