A widespread slowdown in China's economy would have major impacts on the rest of the world, but it's important to remember that the stock market is not the economy (just an imperfect measuring device). The stock markets in China have been very bubbly lately.
My (admittedly limited) understanding is that most economists are still expecting significant growth in China this year, though not as strong as previous years.
Also, the recent financial crisis in the US was partially/mostly driven by a debt crisis (housing/mortgage issues), which historically has had far larger and longer-term impacts than a stock market crash/correction.
The US's whole financial system is tied into its stock market and the financial sector around it (because of leverage and derivatives and every company being public) -- I understand this may not be the case with China? Or am I wrong on this front.
I believe you're correct that the stock markets in China are less directly tied to the economy than than the stock markets in the US.
But, even in the US, I think stock markets are like a balloon tied to the wrist of a toddler on a windy day. They may very generally track where some part of the economy is, but there's too much interference and interpretation to get a precise picture. Even worse, the length of the string is unclear.
My (admittedly limited) understanding is that most economists are still expecting significant growth in China this year, though not as strong as previous years.
Also, the recent financial crisis in the US was partially/mostly driven by a debt crisis (housing/mortgage issues), which historically has had far larger and longer-term impacts than a stock market crash/correction.