The question wasn't whether or not it would be believable, but whether or not a world that operated in such a manner would
qualify as fantasy by virtue of having such different rules from ours. And the explanation... well read below.
So IYO, no amount of exaggerated unrealism would qualify as 'fantastic'? I find this a little odd... doesn't having magic in a setting qualify it as fantasy because it makes the world follow different rules than the real one (our own)? So why wouldn't humans following different biological laws than ours qualify the setting as a 'fantastic' one with different rules?
Hypothetically I would say it's mainly humans' physical limits that are increased in this type of setting. So yes you could have a super strong weightlifter who's not a warrior, or a super fast messenger (some warriors would super fast too depending on their style, and most of the elite ones would have at least fast reaction time). Only the most dedicated and talented ones though in both cases just like not every warrior is Beowulf.
There could possibly be some animals that are the 'alpha of alphas' in their species but for the most part, this is about humans with different biological rules than us. And the reason is they are biologically different (have greater potential for physical development) in that universe.