This is like describing socialism as being about authoritarian governments and centrally planned economies. Everybody misuses labels to their advantage.
While GDP (PPP) of China and USA are similar, this isn't the same as saying that their wealth is similar.
The USA's net national wealth is about $85 trillion, while China's is about $22 trillion. I have a feeling that a much larger proportion of the USA's stock market is held by foreigners compared to China.
It is possible that drops (or raises) in the Chinese market actually affect Chinese wealth more than in American markets...