The animal was not fatally shot so it's still alive but unconcious, like most things or anyone would be, after being shot in the vitals by a high powered rifle. Sometimes the deer will recover or wake up from the initial shock. Huge amounts of adrenaline then get secreted from the sight of predators (humans) so close to it, that it gives its heart added energy, temporarily enabling it to get up and run.
When I used to go big game hunting, a buddy of mine always brought a stethoscope with him! The same thing had happened to him when he got his first deer and scared the crap out of him. It wasn't a whole hour like Dave, but about 10min. later the buck got up and tried to run away while he was posing for a picture next to it. Well he happened to get another deer one time him and I went out (in '89), but he was afraid to get up close with the stethoscope and listen to its chest. I was cracking up. He thought the deer might jump up again and injur him. He got scratched a little in the arm the last time when the buck got up because he was holding its antlers posing for a shot with 1 hand and the rifle in the other. He got knocked back to the ground and also dropped his rifle when the deer got up. The stethoscope's tube is only about 16" long and he didn't want to risk it again, so he kicked the animal for like 5min. then waited another 1/2hr before he started field dressing it. It was hilarious. He had deergetupophobia ever since