You are right. What they are doing is not possible by using the normal Graph API or/and the FQL.
However, Facebook also provides support for two other APIs:
Access to these APIs is restricted to a limited set of media publishers and usage requires prior approval by Facebook.
I think that they are using the Public Feed API. The documentation of the Public Feed API lists some of the publishers that have been using this API and the site you've mentioned in the question is not in the list. The documentation also doesn't mention anything about getting the Page Insights, but I think it might support this feature (as I see no other way of doing it).
Or, they might be using any other such restricted API which is not yet available to the public and not even documented on the developers website, but is currently in beta/testing phase.