That obviously was a not hit in the mythical " dead spot." It was a shot gone awry, hitting the buck in the shoulder area. Obviously, the wound did not heal (may have been due to the broadhead staying in the wound for a time) and became severely infected, then possibly becoming gangrenous.

All wounds are not always immediately fatal. I have seen mangled deer, mangled from being hit by a car, and deer with a leg shot almost off survive for a long time. Eventually, infection, starvation, vulnerablility to predators, etc, takes its toll.