Gonzo is life over the edge. Gonzo is taking things too far just to find out what happens. Gonzo journalism is another name for what Tom Wolfe called "new journalism" which is basically personalizing a story by recounting not just the facts the journalist sought but what the journalist went through to get those facts, giving the reader (or viewer, new journalism has rewritten the concept of documentary TV and movies) a view to what happened to the guy giving you the story, letting you know that the best way to get your event covered favorably is to give the press access to an open bar. Gonzo is something you either get or you don't, gonzo is understanding that HST probably actually shot that typewriter... more than once.
It sounds like gonzo is just one type of personalized journalism. I don't object to putting a journalistic piece's narrative into first person. There's a diary style. But it has happened more than once that I find myself reading what kind of wine the writer ordered. A fatal violation, I won't continue reading it beyond that point.