Yeah, and the amygdala has specific functions. Not that it's the only piece needed for that, or that it's not good for anything else.
The evidence for more advanced brains in higher mammals is also plainly there.
The author seems to be over-stating all this stuff in order to reject it.
And it's also the case that even though certain brain functions are linked with specific locations, the brain can still use plasticity to re-organize things and adapt to damage. And when you're doing any language related task, there are always going to be other more domain-general brain functions involved too, which aren't as localized.
https://en.wikipedia.org/wiki/Wernicke%27s_area https://en.wikipedia.org/wiki/Broca%27s_area