This is interesting in as much as it shows how such thinking has changed over the years, but her real purpose seems to be to create doubt in the reader's mind about whether selection at the level of the gene is the only mechanism of evolution, which is what Mr Dawkins and his fellow selfish-geners believe.
The book is a polemic, and its main target is what Mr de Waal takes to be a distorted idea of human life as relentlessly selfish and ruthlessly competitive.