I'll have to read the book to see if De Waal addresses this issue differently - but there is one glaring omission here that seems to destroy the entire argument. Human language and internal thought (the infinite use of finite means) appears to be entirely unprecedented in nature. This ability appears to gives rise to our heightened creativity and ability to model and understand the world. It is usually the first thing mentioned when psychologists talk about a "special cognitive ability" or "secret sauce", so you would have to address it if you want to make a reasonable point here.
...a better way to think about other creatures would be to ask ourselves how different species have developed different kinds of minds to solve different adaptive problems. Surely the important question is not whether an octopus or a crow can do the same things a human can, but how those animals solve the cognitive problems they face
Humans can solve problems beyond those faced in their immediate environment for survival purposes - that is the key mystery that causes us to compare other animals to ourselves. Sure, we should strive to understand the ways in which an octopus solves the problems it faces, but there is nothing wrong with asking how close it is to our own abilities in this regard.