As stated in the Intro Syntax textbook, the statement is biased; or, if you prefer, it's a category error.
In a case system that uses Ergative and Absolutive case names, there is no such thing as a "subject" or "object". It's precisely equivalent to the statement
- OBJECT is the case of A – the absolutive of transitive verbs. SUBJECT is the case of both A and E, the absolutive of intransitive verbs and the ergative of transitive verbs.
In other words, ergative/absolutive systems don't normally have a category "subject", just as
nominative/accusative systems don't normally have a useful category "absolutive". Every clause has a subject in one system, and every clause has an absolutive in the other; and in both systems there are specialized cases that occur only with transitive verbs.
As for the etymologies, ergative comes from the same Greek root as energy; with transitive verbs, the ergative is normally the agent (prototypically human), and in many languages this is generalized to a mark of agency or volitionality with various verb classes and constructions.
Absolutive, on the other hand, is a generalized replacement for many other earlier names, including nominative, for the most common, default case in an ergative/absolutive system, which, besides being theoretically "the unmarked case", is often actually unmarked. Some preferred nominative because in split-ergative systems like most Pama-Nyungan languages, where the nouns use an ergative/absolutive system while the pronouns use a nominative/accusative one, the same morpheme often shows up as both absolutive with nouns and nominative with pronouns.