"The Internet doesn't use MAC addresses, and Internet packets don't have MAC addresses" is a wrong assumption. What's an "Internet packet"? Without MACs there's no networking. Without networking there's no Internet.
True. In the Second Edition the Preface mentioned that "Finally, the number of UNIX installations has grown to 10" and some of those systems were connected mostly via telephone lines.
The article refers to a "typical packet found on a typical network" then describes an Ethernet frame, so the author clearly refers to MACs in an Ethernet setup.
MAC is part of the Ethernet standard. The clue of why is needed for is in the name "access control". Without MAC there's no Ethernet. Without Ethernet there's no Internet.