There are a few key flaws in your analysis, and none of them have to do with what type of government rules in Beijing:
1) China only opened itself to capitalism, via the Special Economic Zones, in the 1980's. Its capitalism is new, and thus its growth is new.
2) China's annual growth rate is higher than any nation in the world, at 11.5% annually before the economic downturn, and is predicted to remain at approx. 7.5% through to the end of 2009 (and that is considered a 19 year low!). It has enough internal momentum to sustain large gains as its market is based on real assets.
3)
China's GDP is 24 trillion RMB which equates to approximately $3.5 trillion USD annually. That is nothing to scough at for a "third world" nation.
4) The per capita GDP that you have provided calculations for is based on population alone. Of course China's will be less, it has a billion and a half people!
Additionally, your assessment of its command economy is flawed. China, for all intents and purposes, is now a capitalist economy with free enterprise. The government controls very little in terms of business expansion and investment. The Communists largely continue to control social policy in order to prevent the capitalist flow of profit from being disrupted.
That is the modern China, and not the one you have described.