Others have given great answers, so I'll just support their answers with this diagram and a little further background on how to think about relatedness in evolutionary context.
Since the author in this excerpt makes no mention of Bonobos, I would imagine that, by chimpanzee, he really meant the genus Pan, which includes both Bonobos and Common Chimps. But that does not necessarily matter.
Relatedness, in modern taxonomy, depends purely on common ancestry, not necessarily on similarity of specific traits. As others have explained, we make theories about ancestry relationships based on many criteria and logic, not just variation in one gene. In this tree, you should think of A, B, and C as theoretical, extinct common ancestors of the species below them in the tree. The list of apes at the bottom represent the relevant extant species species only. 882
Bonobos and Common Chimps have a more recent common ancestor (C) than either Bonobos and Humans (B) or Common Chimps and Humans (B). This is why <PERSON> said that both qualify equally as most closely related, because the common ancestor of each pair is the same.
Few would disagree that Bonobos do seem to be more similar to humans than Chimps are to humans, but that actually does not mean they are more closely related evolutionarily! Theoretically there are two ways this could happen even if Bonobos and Chimps are equally related to humans, either our common ancestor with Chimps and Bonobos also shared the traits we have in common with Bonobos and Chimps changed, or Bonobos and Humans happened to develop these similarities independently. The former is a simpler explanation, but either are possible for each similarity. Again, the key in understanding this is in thinking about the theoretical ancestor species, B and C. The only way Humans could be more closely related to Bonobos than chimps is if the common ancestor, B, was a descendant of C, which seems extremely unlikely and as far as I know is not supported by the genetic research in this area.
Our common ancestor with Gorillas (A) on the other hand is much "earlier" than our common ancestor with Chimps and Bonobos, so Gorillas are less closely related to use than the group containing Bonobos and Chimps. 404