The important part of that quote is "for the entire IP packet".
That is, the main difference between AH and ESP (without encryption) is what parts of the IP packet are covered by the ICV. AH's ICV covers the complete IP packet, except some parts of the header (like the TOS, TTL and checksum fields). On the other hand, ESP's ICV only covers the payload of the IP packet beginning with the ESP header.
For example, in tunnel mode, it does not cover the source/destination IP of the outer IP header, but the complete tunneled IP packet is covered by the ICV and integrity protected and authenticated.