> What animal would you pursue jogging?
Any animal that sprints for short distances :)
Nearly all animals built for sprinting don't have the endurance for sustained evasion. If you've ever chased wildlife, you'll notice they quickly zip away, but stop some couple hundred meters away to turn around and look back at you. This is really to recharge their batteries and keep an eye on the threat (you).
I mentioned it in another comment, but persistence hunting was a well-known tactic across the world. It's particular effective on flat desolate land, but was also practiced in hilly woodlands, in combination with tracking skills.
Eventually the animal would keel over from exhaustion.
Don't fall too easily into this Paleo trend and the hunches people posit as "the way things were". They often have a narrow view of how things were.
Remember to keep your skepticism healthy. When someone tells you to use a standing desk, because cavemen used standing desks, remain skeptical. When someone says you should just do short sprints, because that's what cavemen did, be skeptical. I'm not saying standing desks and sprinting are bad, I do both, but question & verify what you're told, especially before spreading that (mis?)information.