It's an academic exercise, certainly, and fraught with all the difficulties of categorizing anything (like folk music, for instance...).
From the review:
The loose boundaries between Levitin's categories, however, can sometimes lead to a certain slackness in his argument. By his own account, Levitin places the Johnny Cash song "I Walk the Line" in three different categories, citing it as an example of a friendship song, a knowledge song and a love song. And his criteria for identifying a friendship song — essentially, any music that helps facilitate, prompt or motivate "synchronous, coordinated" movement — are so broad that '60s protest music and chain-gang laments turn out to be friendship songs, too.
War... not having the book's definitions in front of me, I'd guess they'd tend to fall under "songs of knowledge", that is, songs describing life, with or without an implicit or explicit lesson (my own guess at a definition), though some might be more love or friendship related.