I think its all to do with $$$. Having more $$$ for better facilities and scientific research into performance optimization is a force multiplier on top of hard work and determination. Spending the $$$ on foreign coaches who has done it all before in the field also helps, mostly on building the temperament that only experiences brings.Other countries are slowly encroaching into sporting areas where China once significant presence. Chinese women have the right physical build to compete in the singles and doubles in rowing and paddling where power to weight is more important than in the bigger boats.
I don't think genetics have much to do with it at all, given for 1.4bil, there is always going to be some freaks of nature that comes once in a generation, much like Yao Ming, or Liu Xiang. Only when the country is rich enough would there exist the remote possibility that such talents can be discovered and harnessed in the field that their attribute will excel in. Some of the other countries are rich too, so they can also do the same in those fields, such as hiring Chinese coaches etc, hence the narrowing of the gap. Still though, there is that 1.4 Bil pool of talent to tap versus a fraction of that for everyone else. Unfortunately it doesn't work for football though.....