Humans also had one advantage: sweating. We are almost the only animal that can perspire across the bulk of our skin. So we can keep walking/running in the heat of the day when our prey and our predators cannot. Given enough time, in hot weather, humans can harass and run down uninjured deer and even horses. Our method of walking may not be efficient, but our ability to handle heat means we can keep moving long after everyone else has to hide in the shade.
Just look at anyone walking a dog on a summer day. The dog is probably panting. The human is not. In a distance race, the human could easily outrun the dog.
There was not a single new ability which ensured that humans became the most dangerous hunting animals, but an ensemble of correlated abilities, and improved sweating was certainly one of them.
Regarding the dogs, that is why their relatives are seldom important predators in warm climates.
Even the best adapted to warmth among canids, like the African hunting dogs, have to remain much smaller than the large wolves of cold climates, for adequate cooling.
When you compare humans with African predators, humans still have better cooling, but the difference is not so large as when you compare them with domesticated wolves, a.k.a. dogs.
Just look at anyone walking a dog on a summer day. The dog is probably panting. The human is not. In a distance race, the human could easily outrun the dog.