What is the importance of storytelling in war? In The Things They Carried, I think it's important because it comforts the men in time of war.
First, it's important to remember how O'Brien defines a true war story: it has no moral, it has no point, and if it's easily understandable, it probably is not a true war story. Among other things, O'Brien says that "In many cases, a true war story cannot be believed. . . . Often the crazy stuff is true and the normal stuff isn't. . . ." Because civilians life in a world of order and comfort, they are simply not equipped to understand the chaotic world in which soldiers live and die. If O'Brien is correct that true war stories "make the stomach believe," only soldiers who have lived the experience can truly understand a war story.
Having said that, I think you're on the right track in saying that war stories comfort men in war. Even though men in combat get their experience first hand, their experience is clouded by the chaos of war, sometimes called the "fog of war." This chaos generally prevents them from knowing anything other than what happens immediately around them, and that's why, according to O'Brien, when they tell a war story, they can only tell someone what "seemed" to happen rather than what may actually have happened.
They live in such a chaotic existence that the only way to impose some order on their lives is to tell themselves what they think went on in any given situation. The story about the men who went out to a listening post and heard what they thought was a cocktail party in the jungle is a prime example of what "seemed" to happen but obviously didn't. The story teller later admits that he made up most of the story but that it was true nonetheless, and the listener simply accepts the validity--the craziness of it--if not the facts. Sharing the burden of a chaotic life is comforting.
Soldiers (any combatants, for that matter) are comforted by sharing their chaotic experiences primarily to make some sense of those experiences, as well as to have the listeners validate the story-teller's belief that the experience is not understandable--it just is.