I'm fairly sure it's authentic. I wondered how it was possible given the age of those veterans, but apparently some Civil War veterans lived a very long time. There were a lot of them still alive in the early 30's, and the last ones died in the 1950's.
This film clip is mentioned in an article in Smithsonian magazine (
http://www.smithsonianmag.com/history/civil-war-veterans-come-alive-in-audio-and-video-recordings-97841665/ ), and I've seen another short clip from the period that a group of reenactors used to reconstruct the yell (it sounded different and a bit bloodless compared to what is going on here).
Finally, the film clip itself is posted on Smithsonian Magazine's website (
http://www.smithsonianmag.com/videos/category/3play_1/what-did-the-rebel-yell-sound-like/?no-ist ) . For those who aren't aware, the Smithsonian is more or less the official keeper of the American heritage (and is sometims refered to as the nation's attic), so if they posted it, I'm inclined to think they did their homework.