There is, of course, a lot of qualitative judgments to be made in such a categorization, but there are, I think, two key questions that one can ask to determine if a country is a core or peripheral one in a world-economy such as Braudel and other thinkers influenced by him would frame the issue:

1. Is China a world banking center yet, or merely an internal or regional one?

2. What import does the the prosperity of that country have to the prosperity of the core countries?

On question one, China engages in two kinds of capitalist finance primarily.  It finances its own exports and it finances its own internal construction boom. To an increasing degree, China is also purchasing assets abroad, but I think that to date most of these assets are in other peripheral countries, not in core areas such as the US and Europe, although this is changing as time goes on.  China is not yet a banking center comparable Japan, the US, or the UK, and until it becomes one, capitalists won't opt to raise and organize money in China.

On question 2, I think China could collapse entirely today, with financial meltdowns, famines and social unrest, similar to Russia in the 1990's, and the core economies of the capitalist world would feel few, if any, severe reverberations because of it. That just cannot be said of the large core economies of the capitalist world, particular of the United States.  While China has a very large stake in the prosperity of the capitalist world, the capitalist world has only a minor stake in China. China represents the risky, venture capital part of the portfolio of the capitalist world, not the patrimony, which is the US, Europe, and Japan.

Wallerstein, in my opinion, has always been mislead by his anti-Americanism. It prevents him from effectively using world-systems theory in an honest and therefore useful way.  Nothing in world-systems theory, for example, hypothesizes that tiny countries like Greece have the kinds of deterministic outcomes on large core countries that he implies here. Greece just can't matter very much to anyone who has more than one degree of separation from those events.  So I think he'd be better if he stuck to the rules of his own methodology.

And we just had the "mother of all financial crises," according to the same Barry Eichmann that he's quoting, so I wonder whether he's taking Eichmann out of context -- I don't know, I like to see his source for that and maybe Eichmann is getting caught up in the hype now too as many good economists have been.

Like the "Europe is doomed" narrative we all make sport of here, Wallerstein's "capitalism is doomed, especially America" narrative seems to lead to overly selective analysis of the facts, from my reading of him anyway.

But either way, even Wallerstein seems to side against he idea that the center of capitalism is shifting to China.  Rather, capitalism is imploding and going to take China with it seems to be his thesis.