I found this diagram in the JSON specification:
(source: json.org)
Where does this diagramming convention come from? Is it just some random convention cooked up by D.C.?
That diagram is known as a syntax diagram or railroad diagram. It's used to visually represent context-free grammars. It's a graphical depiction of the Extended Backus-Naur Form, which is also used to represent context-free grammars.