I don't believe that the amount of structured data is the criterion at all. Google (and any other search engine) has its own criteria for what it considers worthy of KG inclusion or treatment (actually, I believe the structure is recorded; the question is really about display). My own web site, for example this article,
http://www.mkbergman.com/1847/shaping-wikipedia-into-a-computable-knowledge-base/, has oodles of
schema.org structured data, as does my entire site, and it does not display. Mind you, I don't begrudge whether or how the search engines make these decisions. The fact they are supporting it is a good thing.
Mike