This is something that cannot be overstated, they are in an incredibly dangerous position given what has happening at home, the rampant corruption that infects everything, the leftover politican fun of communism with its day-long murder "trials", the lack of any kind of force projection to protect these assets they are buying up around the globe, and the incentive that nearly everyone else in the world has to default.
From what I've read, the PRC government does stick its fingers in many pies. But I honestly doubt they care about world domination.
http://www.prospectmagazine.co.uk/politics/mark-kitto-youll-never-be-chinese-leaving-china/A xenophobic government might attack its neighbors and conquer them. But they tend not to Imperialistic World Super Power state like the Romans, Mongols, Byzantines, British, Ottomans, etc. You need to be pretty accepting of the local wogs. Sure, you also need to believe YOU are superior to everyone else in the world, but you need a pretty flexible system in order to accommodate the local cultures in all the random places your Empire takes. That's the mark of every successful Empire in the history of the world. Otherwise, they get smashed sooner rather than later. The exception is "kill everyone and everything, then repopulate with your own folks". Not likely to be successful these days with advances in weapons. Ask the USSR when folks with little more than rocks, spears and AKs decide not to accommodate foreign invaders.
I don't think the PRC government has the mindframe to become a political or military superpower. Too rigid, too xenophobic, too self-centered as a collective, etc. Economic superpower, perhaps. It will be interesting.
I have long suspected that the PRC is rigging their books. No one will know until long after it pops just how rigged their game is.