It seems the authors (or ADN editor) left out some important context in this article.  China (yet not America, sigh) is a signatory of the UN Law of the Sea Convention.  As the article states, the treaty sets territorial waters at 12 nautical miles from shore.  However, the law also sets that "shores" do not include artificial islands made from uninhabited corral structures or lifeless "rocks."  It also extends that possession 200nm for exclusive economic usage.  China violates this part of international law as well by claiming the entire South China Sea including parts well beyond China's 212nm claim and well into various other nations like Vietnam and the Philippines.  IIRC China lost a case a few years back in regards to its claims.
Regardless of how legally empty its claims are it still calls on other nations to respect their claims with threats of "You are causing an international incident."  The US rightly enjoys free navigation through most of the South China Sea.