He shoulda had a big knife at hand, just in case...
Most serious hunters I know carry a big hunting knife because sometimes you come across the deer (or whatever) you shot and it's not quite dead. So you use the knife to finish it off.
A bowie knife would have done that hunter some good once he finally figured out he ought to drop the bow. Then again, the only way to face an animal like that is to either run/climb to some sort of shelter, or try to go on the offensive and beat on the animal until it decides it has something better to do.
It's not like the deer wanted to eat him, it just wanted a fight.
A knife or even a large stick would have worked, if he'd had the right attitude about the whole thing. The really funny thing is that although he was trying to shoot/kill the thing before, when fighting it by hand it looked like he was trying to avoid hurting the deer at all costs. No kicks, no strikes, nothing. Just some weak pushing and blocking. At the very least, a size 12 boot or gloved fist to the nose might have given him enough room to stand up and run, or make the deer pause long enough to come up with plan B.