Yeah the guy with the gun works for the US backed South Vietnam government. He was the police chief. And this was right after/during Tet Offensive in Saigon. The guy he is shooting was Vietcong. I took(and passed) a college class on the history of the Vietnam war and this is one of the things we learned about.
It looks real bad shooting a man point blank in the head when he has his hands tied behind his back. But as I understand the North Vietnamese man had just killed a bunch of the chief's men. And you know how unpset cops get when one of their own is killed. So I totally understand, and at least he did it quick and easy.
Here is a quote by the photographer
The general killed the Viet Cong; I killed the general with my camera. Still photographs are the most powerful weapon in the world. People believe them, but photographs do lie, even without manipulation. They are only half-truths ... What the photograph didn't say was, 'What would you do if you were the general at that time and place on that hot day, and you caught the so-called bad guy after he blew away one, two or three American soldiers?
And goes on straight from wiki ;)
Adams later apologized in person to General Loan and his family for the damage it did to his reputation. When General Loan died of cancer in his new home of Virginia, Adams praised him: "The guy was a hero. America should be crying. I just hate to see him go this way, without people knowing anything about him"