Heart and lung capacity,ability to provide oxygen at a high rate of consumption . White tail only good for a short distance.
Given the right terrain deer can be tired out by any one capable of long distance running. Deer must be steadily pursued and not allowed to rest. And yes i did run a deer till it dropped in the snow twice before leaving it. That was long ago and when i had two legs. Cornered others in fence corners. No i did not kill them but a rock would have sufficed on one.

How far have you ever chased one? Even not running get where you can stay on the same animal (not easy to do,area and snow both important) at a good pace and keep it moving. When you see the reaction hours later i hope you don,t like it .besides your facing a stressed animal as far as quality eats.
Not a concern in our not so distant past.