Apparently under Georgia law if it is a felony you only have to have reasonable suspicion to make citizens arrest. Andrew Branca has done a video blog on the video that I am about half way through and his conclusion so far is that it may be justified based on Georgia law.
Whether this is justified or not may depend on evidence other that the video like what was the demeanor of the two shooters, were they threatening or what. If somebody walks up to me with a shotgun, even though they may have the ability and opportunity, I may not be in jeopardy (AOJ triad), and therefore it would not be self defense if I shot them. Apparently the victim was not a choir boy and was on probation for carrying a pistol on an educational campus and obstructing a law enforcement officer and one of the shooters is a former law enforcement officer who may have had prior dealing with the victim.
Do I think the shooters are morally right, no, I do not think so. If it was me I would have let the guy go, and called the police. But what they did may be legally justified under Georgia law. It brings me back to an altercation I had a few years ago. My father was checking out his deceased mother's property when I homeless person took a swipe at him with a knife. Luckily he was not injured and came over to our place of business and told me. I jumped in my truck and followed the person attempting to call 911 on my phone a the same time. He stopped at a side street and I pulled in after him and then he proceeded to continue his walk up the main road. I turned around and continued to follow him and flagged down a highway patrolman who happened to pass me and informed him what happened. He was able to stop the guy and took him into custody until the sheriff's deputy arrived. In this instance no one was hurt, but it could have turned out like the one above. What if the guy would have took a swipe at me with the knife? Would I have been justified to defend myself, or would somebody exclaim that I should not have been following that person, just let the police handle it, when more that likely, if I would have, they would never have caught the person. Food for thought.