Joel, thanks so much for posting the pdf.
I purchased the Carl Fischer score from
http://www.sheetmusicplus.com about a month ago. That version was edited by a Joseph Glahm. It's very interesting to compare that score with the one you posted, which I assume is how Sgambati originally notated it.
The Fischer edition uses only two staves and the editor clearly shows what notes each hand should play. Yet when I look at that version, it gives me absolutely no sense of what the piece is about.
Now that I have seen Sgambati's original notation, I have no problems whatsoever understanding his intentions.