The Chinese are clearly in the wrong on this one. You just don't do the sort of stuff they did to other sailors; it puts them all at risk of inury or death. And this incident is of course not the only one.
The PRC can claim that its EEZ is territorial water as much as it wants to, but it remains just that: a claim. The world does not recognize such a claim on their part. Under the LOST, the EEZ grants exclusive economic rights to the possessing nation, i.e. the right to exploit natural resources. The possessing nation does have the right to stop activities which go against this, such as unauthorized foreign fishing vessels conducting fishing operations in such waters (the Cod Wars come to mind). However, all rightful claims to authority end there. Ships can travel freely in such waters and can conduct any activities that are not those previously mentioned, and are not otherwise illegal under applicable international laws (international laws, btw, cannot lawfully be applied to non-signatory nations). Observing other vessels, on or below the surface, is not illegal in international waters, regardless of whether it's done visually, using radar, sonar, or other instruments. That the PRC does not like it is rather irrelevant. Such observations are passive, and thus cannot be considered an act of war. PLAN and other Chinese maritime vessels' actions are wholly unjustified and unlawful.
Unless China wants to go to war over the issue, it cannot legally do anything, even if they percieve the actions of the USN ship, potential or actual, to be a threat to their security. For those playing the national security card, they should keep in mind that the U.S. military also views the PRC as a potential threat in and of itself, which is partly why it is engaged in these activities.