The stock market primarily reacts to what happens in China, and so a collapse in China will shake the faith in the NYSE and other exchanges.
The US Stock market has the potential to collapse this year, just like it has every other year. The difference right now is that we're experiencing one of the poorer events that can happen in the worldwide economy, and thus there's more chance that it can collapse.
It all depends on investor confidence.
Confidence for sure is a major component, but we're not simply mirroring China's market. Sometimes China's losses spook investors in the US (on the confidence point) but on the whole, China's stock market is a giant sham propped up by their government, and it will see many bad days ahead while the US market will continue to trade on data more relevant to US investors.