Several reasons can be proposed:
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. 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). This is actually the explanation given by the directors in one of the making-of documentaries on the dvd.
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.
2) He was from a different tribe whose traditions didn't envolve marking each other with Alien blood, like Predators in Predator and Predator 2.
3) The mark means you are a proven highly ranked Predator Hunter and there are probably many different Predator tribes. 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. The Predators on the ship could have been lower ranked hunters or Predators scientists.
The reason why the Predators in Predator 1 and Predator 2 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.
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. In AVP1, 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. 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. It would make more sense for the Predators to hunt humans first, then if they are successful, hunt aliens after. Because Humans are relatively fragile, most wounds are enough to cripple a human. 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. 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. (originally for the first Predator film, humans were called the 'ultimate prey' but that was just the movie's slogan and put forth before the concept of AvP)
Maybe Wolf Predator was never eligible for the Alien hunt because he was weaker or not from a distinguished tribe. When he saw there was a situation involving escaped Aliens, he may have seen a long dream come true to hunt the ultimate prey, and went in without asking permission.
5) Perhaps Wolf Predator is a disgraced hunter who has hunted Aliens before, but then messed up something, causing the other Predators to demote him to his current 'cleaning' duties. That would mean they took away his marked helmet (if he had one), and also the mark on his face by scarring the surrounding tissue (if he had one, see reason 2). So he may have a low function, but still have considerable experience in the hunt for Aliens.
6) How the Predator in AvP marked himself and the girl was taken from the book AvP:Prey. In this book it was explained that a Predator who had hunted his first alien would be blooded by the leader (with the leaders mark). This was a way of signifying a caste system within the hierarchy and show other Predators who had trained you. AvP took some creative liberties from the book, and other movies simply may not have included this backstory in them. Though in AVP1, the leader Predator was Celtic and he was killed and Scar marked himself so being marked by a leader may not apply to the movies.