Here are the books mentioned in the article if you don't care to read it in its entirety.
Redeployment, by Phil Klay
Thank You For Your Service, by David Finkel
Letter Composed During a Lull in the Fighting, by Kevin Powers
Dust to Dust, by Benjamin Busch
My Life as a Foreign Country, by Brian Turner
Packer also recommends a 1968 collection of stories by Tim O'Brien titled The Things They Carried, as well as his novel Going After Cacciato.