On short distances all dogs outpace humans. After an hour of running most dogs will just quit. On several occasions I had very hard time convincing various dogs to get off the ground after an 8-10km run.
I used to believe in the endurance hunting thing until I realized playing with my dog it didn't make sense. They DO get tired, but they take a 1 minute break and it's like they are back square 0.
For the record, I'm in shape and with a pretty light frame (181cm/70kg) and go for 10km/1 hour jogs regularly.
Try to play with your dog for an hour at high intensity. If your dog belongs to a large or very large breed it'll get tired much more quickly than you - assuming you're in somewhat good shape.
I'm not advocating in favor of endurance hunting, I'm only stating that we can out-endure some large-ish animals.
[1] https://www.irunfar.com/aleksandr-sorokin-smashes-24-hour-wo...
Still, this is an exception to the rule - overall humans outperform almost all animals when it comes to endurance running.