I'd say it's a category, not a degree. I.e. humans aren't "just animals".
You are right. As was mentioned before, we have a need for recognition, but not due to any evolutionary history. This need arises only with self-consciousness, and therefore it is inherently human. You need to be a person in order to have such need. Sure, it may be that great apes achieved some degree of self-consciousness, bu it does not demonstrate that humans with full-blown self-consciousness are mere animals. It actually shows that the great apes are on their way to personhood, and, probably, should not be treated as mere animals.
I wouldn't take all anthropologists say, as a final truth, because they change what they claim with each passing generation of scholars. I was an anthropology major first, but I got tired to hear that all our motivations come from survival and need for procreation. My experience tells me that when we want to get laid, a lot of healthy offspring is the last thing we want 95-99% of the time. Sure, they told it was not conscious, and whatever people tell about their motivation for having sex, they simply do not know it. But this position pretty much makes this theory unfalsifiable in principle (what exactly would count as dis-confirmation that they would accept if they postulate an operation of some hidden force that is not accessible to any conscious experience?), and, therefore, it is not a scientific theory anymore.
Eventually people even in anthropology came to see reason, and started to pay attention to our conscious social needs. People have a lot of needs, and they go way beyond mere survival. All this puts human animals who are persons, into a separate category.
May be pleasure (as a category) is something all sentient organisms seek, does not matter what their origin is. But to lump all pleasure together is not fair. Even animals can feel pleasure when they are fed, warm, bathing in a sunshine, with no predators around. But you got to be human in order to get pleasure out of a good argument, great music, beauty, or art. So higher pleasures unknown to mere animals + a conscious need for recognition and original activity (we all want to be authors of our own lives, and create or discover things) + extensive use of reasons and reasoning-guiding, often future-oriented behavior + abstract reasoning + either moral sense or social construction of morality and justice are markedly human (or, probably, of persons of any origin), and clearly separate us from mere animals.