The term doesn't really convey real meaning. It's just a rhetorical sneer. Like, if I wrote "Zach Tellman is basically Microsoft's idea of a smart person." It is somehow putting down the author, and Microsoft, and implying that I'm so much better and smarter. In the same way "He's not a serious public intellectual" implies not only that PG is unserious or non-intellectual, but that the author is some high authority who can cast these judgments.
In reality, of course, the author has no claim to judge who is serious or who is an intellectual.