With the world connected virtually at every corner and side road, it is impossible for the recent issues in China's stock market to not impact Wall Street. Fund managers undoubtedly have a mixed bagged portfolio which would have assets sitting in both China and the US. With such a link, there is no escaping the oncoming impact.
All worldwide business processes are tangential but they are limited in that perspective. The recent losses in China are the result of margin changes to three Chinese companies. This represents a loss of equity to those firms that was not in their power. Other buyers won't consider this a warning or threat but an opportunity to pick up where they left off.
The entire world is connected economically at this point. China's financial problems will have some repercussions on Wall Street, but I wouldn't expect them to be too dramatic. China's questionable business ethics (read: they lie like their pants are on fire) are well known around the globe, only high risk players are going to get burned. It would be a small correction.
China's plunge will cause some damage. This is because we are heavily reliant on the economic performance of other countries anymore. Perhaps 100 years ago this was not true, but all regions are linked now, and if one country does badly, then many other countries are right behind them for a fall.