Why does the -OH group in β-naphthol direct the incoming diazonium salt towards the ortho position?
It's sort of a process of elimination.  The electrophilic ion could potentially attack anywhere, but:


The hydroxyl group is activating, so the electrophile will prefer that ring.  You are left with three open positions.
One of those three is meta to the hydroxyl group and so less favored, as activating substituents are generally ortho/para directing.  Hydroxyl follows that rule.
Finally -- electrophilic substitution in a naphthalene system is kinetically favored next to the other ring.  See here for example.


We have one position that's on the same ring as hydroxyl, ortho or para to that hydroxyl group, and next to the other ring.  That is the position shown in the book.