We have brain circuitry that facilitates that ability. They do not.
Broca's area, when damaged, makes one talk very similar to how an Ape who has been taught sign language does.
Wernicke's area, when damaged, while Broca's area is not, renders someone who can speak fluently and without labor... but makes no sense in the words they are using.
The apes seem to have at least a somewhat evolved Wenicke's area, but absolutely no Broca's area.
The important factor here- is even a person, with both of those areas damaged, is likely just as intelligent and emotional as they were before- but you would never know, by anything but their facial expressions.
Our ability to process language and speak in complex syntactic structures isn't a product of our intelligence, it's some very specific brain circuitry that evolved out of our existence as a social species that wasn't very high on the food chain.