Self awareness is the ability to recognize oneself as an individual. Some humans are self aware, so are some dogs.
Self awareness is recognized in most great apes, elephants, cetacians, ravens, gray parrots, and octopus.
Another sense of intelligence is the ability to solve multiple step problems; again some humans are capable of this ability, as are some dogs.
The same species listed above also have this capacity.
As for the basis for humans being unique--it took us a million years to develop a written language--once that happened some humans became capable of working multiple step, multi generation problems, with solutions that can lead to our own extinction.
Human uniqueness then will be as the first species that committed suicide.