Well, it looks like they tried, hence the chest tube, cut open chest and rib retractor. The final two pictures are what they found when they cut him open. However, he ended up croaking anyway, as seen in the second picture where he's been sewn back up again.
I only know the shooting took place in South Africa, and that the doctors worked pretty hard to save his life, but the bullets transected too many organs for the poor dude to make it.