If he has no tools, why would a bison run from him? What is he going to do if it doesn’t run? Spit at it? Call it names? Try to kick it to death?
Bison don’t run from foxes or raccoons, even though either one could do more damage to a bison than an unarmed human. That’s because they know that the best tactic when confronted with such an inefficient predator is to stand still, even if the predator does try to attack, they jut step on it. And that is exactly what would happen to us.
Large animals run from humans because if they don’t run we can kill them with our tools. If we don’t have tools they will rapidly learn not to bother running from us. At that point our ability to run long distances becomes worthless. Nothing bigger then a deer is going to bother running form human if we don’t have tools.
That, at least, isn’t an issue. American Indians used to capture horses by running them to exhaustions and then leaping onto their necks and choking them to unconsciousness. We can kill exhausted animals effectively even without tools.
But once again, why would it run itself to exhaustion escaping something as harmless as a human?
For small animals we have many options.
We can pick them up and drop them over a creek bank or hoist them into a tree and drop them from there. When it goes splat we can eat all the meat we want. Of course if we can run the animal off a cliff that saves a lot of effort.
We can break the bones, and the compound fracture will provide a hole through the skin. Even without any tool at all it’s easy to break the leg bones or ribs of something like a deer by jumping on it or kicking it.
If there are no convenient cliffs or trees around we can simply drag the carcasse a few hundred metres until the skin abrades away.
Once you can make a hole in a hide it’s fairly easy to widen it. It’s making that initial hole that’s tricky.
For larger animals we can wait until other scavengers open the skin and then reclaim the kill. If in our fantasyland are supposing that a bison will run from an unarmed human then a wolf, coyote or buzzard sure as heck will.