"Moments later the victim was approached by two black males in a black four door sedan (possibly a Honda Accord). The driver of the vehicle said to the victim "give me my gun back and I'll give you your phone that you dropped". The victim then used the shotgun to strike the rear windshield of the vehicle causing it to break."
Unless the others in the car were armed, I think it's rather difficult to bargain for an exchange of anything for a firearm that you previously used against your trading partner.
My advice is, if in New Orleans and you happen to successfully pull this move off, get off the street in case he comes back with a bunch of armed guys looking for you.
I know this exact spot. I've walked on Burgundy past Esplanade and in the Marigny several times, even at night. But, I would not have reacted like this had it been me.