Why should we give the number of pages on arXiv?
Page length is one of the most basic things you can know about a document, and one of the few useful numerical measurements of a piece of writing.  I personally find it helpful as an indicator of how "serious" something is.  (This holds for novels as well as papers.)  If I see one set of notes on a topic that are 8 pages long versus another set that are 56 pages, I have a good sense that the latter set is much more detailed than the former.  Similarly, a 6-page paper entitled "Bounded gaps between primes" (a famously hard problem, very unlikely to be solved in so short a work) gives a very different impression than a 54-page paper with the same title.  

While page length is not equated with how deep or interesting something is (and of course depends on format), it can be at least suggestive.  As a corollary, I also take page lengths into account when evaluating job candidates to get a sense of how productive they are.

Regarding the definition, I think it's safe to interpret page length as the number of pdf pages, as this is what most people will immediately see when they open the pdf.  That said, if it's a book, it's perfectly fine to put something like 286+xvii pages, but I doubt people will care much either way.  Remember, this is just a preprint server.