You should be asking "if" rather than "when". All throughout the 80's people were anticipating that Japan would eventually pass the USA. Obviously that didn't happen.
It is not as easy. In the video China looked smaller than it was for a long time, simply because the video measured GDP in Dollar, and the Yuan was heavily undervalued to the Dollar. As JRPGfan points out, it still is and in terms of PPP (what the currency actual can buy instead of exchange values) China is ahead of the US for quite some time now.
You're right that China has issues. But the US does too. The issues for China are, that because of the One-child policy it's population is growing older very fast. US issues include, that they produce not very much themself, but are economically strong for connections with other countries. In fact the economy of China and the US are strongly entangled.