Even if that documentary isn't a fragment of your imagination, you don't know much about the condition of that animal. Besides, real hunters, those who hunt for food, won't be that stupid to chase a prey with one person. They group together, encircle the prey, scare it, and let it run. Since typically a gazelle runs when the predator in a couple hundred meters (depends on the predator), if it see human hunters, it would try to get near it but turn to other direction. If encircled, gazelles run and change directions very frequently, this may very well cause they to fall, rather then overheat and die.