“Seems to me “the press” is a generic term meaning anyone that publishes information/news outside of a book or magazine.”
I see nothing that excludes books or magazines. They are press too. Arguably important ones.
More generally, it is IMHO the right of the people to be someone who publishes information in any format.Journalists promote the idea that they, and they alone, constitute “the press.” In reality when journalists think of the press they mean the Associated Press and its membership. That is an arrogant, elitist view in which they consider themselves to be, essentially, an established priesthood above comparison with bloggers.
The AP newswire is their god - but today, the Internet has vastly more bandwidth than the AP does.