China will most likely grow old before it ever grows rich (aka, outdoes the US consistently and permanently).
China may temporarily pass the US in total GDP here in the next decade. It may stay that way for a decade or two, and then I expect it to stagnate, while the US then passes it (assuming the US ever got behind in the first place) once again for good.
I say this because China is what I call an "Old World" nation. Most nations on Earth are Old World nations (this is not just a geographical locator term, as most nations in the Western Hemisphere are also Old World nations and cultures), by which I mean that their approach to culture and social organization is fundamentally antiquated - they're not set up to keep expanding once their population stops reproducing, either through government social engineering or through apathy. China is an example of the former, while Japan, Denmark, and other northern European nations are examples of the latter. They are all, in other words, truly decadent.
Despite all the talk about its decline, there is only one nation - a New World nation - that is both built to keep expanding into the future and to remain at the top, and that is the United States (and Canada, to some extent, but this is as much a product of its proximity to the US as it is one of its own internal organization). The US is a truly robust society, despite what Twitterites may say, vital and virile, and constantly taking in new peoples. This is exceptionally important, given that our white population, among some others, no longer reproduces at replenishment levels.
So, in short, China may still rise for a bit, but I think it will be short-lived. Its population will soon be in decline - a matter that may not have made a difference had China been at its current stage just a decade ago and had time to get wealthy before the demographic decline - and it will then reach a point of stagnation since there still isn't enough wealth distributed among enough Chinese to keep it growing.
I don't think the "pivot East" ever comes, although it is certainly true there are numerous emerging markets there. Which is like saying that jobless people stand to make money once they have jobs