No, it's not just about EEZs, it's also about security.
There has been a perception that China wants to put military installations on those islands in order to secure their sovereignty. I think it's rather the opposite. Nobody in China really cares much about the SCS islands, so why would the CPC declare them to be a "core interest", on par with Tibet and Taiwan?
The simplest answer would be, because it has vital strategic importance. A strong, permanent military presence in that region would greatly improve China's maritime economic security, made especially important by the New Silk Road plan.