Sled dogs in the Iditarod are given regular rest and food breaks; they don’t run non-stop. If they decide they are too tired to run any more, they have been known to simply refuse to do so.
Actually, there can be only one “primary” purpose.
Primary purposes are very unique. 
This is a good oportunity to link to my favorite all time picture. The hunter has run down the antelope with his dogs and is preparing to dispatch it with a spear. It has several elements mentioned in this thread.
the most perfect picture of being human that I know of
An insightful documentary on the subject.
Great book, I read it after I saw his TED talk and then started running again. The Chia seed/water/line juice/honey drink isn’t too bad either.
TED talk here where McDougall discuss the running man hypothesis. I think in the book he also mentions we were probably running down prey a long time before we had significant tool use, or effective hunting weapons.
http://www.ted.com/talks/christopher_mcdougall_are_we_born_to_run.html
Why do we need to add the caveat that running means on land? There isn’t anyone reading this board that doesn’t know the meaning of run. No one would consider a flying bird to be a long distance runner as the verb run does not mean fly.
Yes. I am unaware of any organisms that can run on air. A few can run on water, like basilisk lizards and water striders.
Yes, but a flying bird can accomplish the same end as a running human, and do it much more effectively.
It can’t catch a horse.
In any case, that wasn’t the question.