China has a whole host of problems all their own. While Mandarin is going to be important for business, it's more the case that it, like other non-Western-European langauges, is criminally underrepresented in much of our schools (and i'm talking private colleges here. My own has a far more robust Italian program than Japanese, Russian, and Mandarin combined), and it's not going to be so over-dominant.
The Chinese government is in an interesting post-totalitarian phase, and is pretty much a pure bureaucracy at this point. While they've played post-totalitarianism far smarter than the Soviet Union did, and lack most of the Union's old economic problems, China's got similar structural issues boiling under the surface, stuff that their government plans to buy off, but these issues will be reckoned with before China can properly take over the world. The most they could hope for at this point is a Cold War style two-power parity system, but China more has to worry about the other BRIC countries, especially the two that are its neighbors, before it can worry about grappling with the USA for dominance.