

Aliens are far more dangerous, they have no fear, can lose most of their limbs and still pose a major threat, they have acid blood, can kill with their claws, tails and teeth and can see Predators even when they're cloaked. They are panicky animals, even the toughest humans could go to pieces from the fear of the invisible enemy and humans can't see very well (compared to predators or aliens) and are virtually harmless unless they have some firepower in their hand. Because Humans are relatively fragile, most wounds are enough to cripple a human.

It would make more sense for the Predators to hunt humans first, then if they are successful, hunt aliens after. It would even seem a waste of talent if a Predator had achieved this ultimate honor, and would then be forced to hunt much weaker prey, like humans. In the previous AVP, the Aliens were called "the ultimate prey" perhaps it is a special privilege to hunt for them, preserved for only the most promising warriors or the noblest of tribes. (4) Although the hunt for Aliens is described as a coming-of-age ritual in the movies, it is never established that every Predator has to go through this ritual in order to become a real hunter.

The reason why the Predators in the first two Predator films didn't have marks may be because they were from different tribes who hunted Aliens, but not mark themselves, which Wolf was probably also a part of. The Predators on the ship could have been lower ranked hunters or Predators scientists. So Wolf Predator could have been from a different tribe than the ones who went down into the Pyramid and did not need to prove himself. (3) The mark means you are a proven highly ranked Predator Hunter and there are probably many different Predator tribes. (2) He was from a different tribe whose traditions didn't involve marking each other with Alien blood, like Predators in the original Predator and Predator 2. Also, his mission wasn't actually to hunt for sport but rather just clean up the alien mess: there was no game or ritual involved.

This is actually the explanation given by the directors in one of the making-of documentaries on the home video releases. Also he may have had the mark somewhere else, perhaps on his cheek, but it was heavily scarred so the mark was lost (or the scars function as a large mark). (1) He may have had the mark on a helmet (as we see he has a vast selection) but he just didn't take that helmet, as he is obviously a seasoned hunter he didn't need to take his original hunt mask.
