Survival of the fittest is just the circumstances we find ourselves in. Our strategy to survive is cooperation. Human are amazing at cooperation, second only to eusocial insects. Fairness is an important mechanism in organizing this cooperation.
"Might makes right" will also force cooperation from those who are less fortunate. I'd argue there was almost never "fairness" in human relationships, from stronger warriors getting the best food to kings forcing their will upon their subjects to filthy rich individuals owning the greatest part of the world wealth today.
My point is in no way that this is right. Only that humans are not intrinsically fair.
So, yes. Fairness is intrinsically human.