The shoal is just 60 nautical miles from the western Philippine island of Palawan, well within the country's 200-nautical-mile exclusive economic zone, as recognized by international law.
The ship that ran aground has been identifies as the frigate Dongguan (560), a Jianghu-V class frigate. Welcome to the South China Sea littorals.
While the Half Moon Shoal is within the Philippine EEZ, the Chinese frigate has every right to be within those waters of the EEZ (but not necessarily on the shoal itself).
Under international law, the Philippines are well within their right to confiscate the warship. But even if it is within their rights under international law to confiscate the frigate, the Philippines really can't do much about it except what the Chinese allow them to do. The Phillipines just does not have the military strength to challenge the Chinese.
You can bet, even with the Chinese on Philippine soil, the Obama Administration will do nothing but watch.
Live Long and Prosper....