The book which Richard calls Rory to talk about is A Mencken Chrestomathy by American author and journalist H.L. Mencken (1880-1956), first published in 1948. A chrestomathy is a selection of literary passages, usually by a single author; in this case it is a selection of Mencken’s own out-of-print writings chosen by himself.
With the phone call from Richard, the audience (and Lorelai) can see that Rory and her grandfather are bonding over books and reading. Rory must have told Richard about her journalistic ambitions when she told him she was looking for the book, and he almost immediately found a copy for her.
It can’t help but put Lorelai’s nose out of joint. In all her years at the inn, her father has never once phoned her at work. Yet after just one morning with Rory, Richard calls his granddaughter to talk about a book while she is working at the Independence.