There are thousands of details in the functioning of every animal cell that are shared by all the animals. The genetic machinery needed to maintain all these detailed functions is pretty impressive and supplies a large margin of commonality. From here we can progress down through the philogenetic tree. Both chimp and human are vertebrate animals. More impressive still is that they are both mammals.
All mammals have livers, kidneys, endoskeletons, hair, noses, brains, etc.
All this similarity must certainly require a lot of genetic machinery that all mammals share in common. We humans are quite impressed with our brains. But we don't know how impressed we are justified in being since we don't yet understand just what uniquely characterizes our brains that is different from other mammals and that makes our abstracting abilities so much greater than theirs. We don't know exactly how the brain achieves those functions. It is a bit early to be too impressed.