Over on Linguistics.SE, there's a question about the difference between deixis and anaphora:
The linguist John Lawler posted a short comment there with a simple explanation. It's short, but in this case I think it tells you just about everything you need to know:
Very simple distinction: First and Second Person are Deixis, Third Person is Anaphora.
It makes sense, right? When I say him or her, I'm usually referring back to someone I've already mentioned:
I'm looking for Jane. Have you seen Her?
But when I say you or me, I'm usually not referring back to anything that was previously said. Instead, you figure out what these words mean from context, deictically:
Hey there, my name's Snailboat! Would you like to buy a vacuum cleaner?
This applies to Japanese just as well. 私 and あなた and so forth typically have deictic reference, not anaphoric.
It does seem slightly strange that Makino et al. didn't take the time to explain this. But if you look, their top-level classification is into "personal pronouns" and "demonstrative pronouns". Then they explicitly define the subclass of "anaphoric personal pronouns". I don't know why they didn't go on to talk about deixis as well—I think it would have been clearer if they had.
Of course, the explanation above is slightly oversimplified. It's possible to use a third-person pronoun deictically. I could specify who she is by pointing ("Hey, what's she doing here?"). But generally speaking the distinction in John Lawler's comment holds.