If the wound is low enough, a very wounded person has a chance to execute a low-skill move like a tourniquet. Plus, since he had a holster, I'm guessing there was a belt around.
What's he supposed to do, turn on the oven, grab a metal implement, find a You Tube video, heat 'er up and start jamming hot steel into a blood-vomiting hole? Thinking cauterize is not a viable option.
Then again, he could have blazed through the other 5 rounds and jammed the hot pistol barrel in the hole (thanks, Cormac).