No and Yes. Some other animals have a diversity in their behaviors and engage in social organization and hierarchies. I don't know if their biology makes humans more inclined to do so compared to other mammals, but humans more capable of creating these complex organizations and/or social structures.
Humans are more adept at using systems of communication for self-expression, exchanging of ideas, organization, and manipulating their surroundings or objects...etc, compared to say a Bonobo (type of chimpanzee). I believe it has something to do with how the human brain and body is structured compared to the structure of other mammal's brains. Although, Bonobos can do similar, but not as 'advanced' you could say. They're capable of communication and/or self-expression, which are either done by visual cues/facial communication and/or vocal (pitch and type of sound (i.e. bark, grunt, whine...etc). They do have social organization usually with the female as the alpha or at the top and sexual behavior is used for more than reproduction, but also for status in the hierarchy, games, stress relief, and all around fun. The male alpha must gain the acceptance of the female alpha to be the male alpha. They use basic tools and can manipulate their environment also, but not as complex as humans.
tl;dr humans are more advanced and capable than bonobos.
I don't know if that even came close to a rational response to your question. If this is your reaction, I don't blame you. :P I took inclined (or allow) to mean capable and I like Bonobos.