All of these animals were taught to sign in order to get food, tickling, grooming, toys, and to get out of their cages. The question, then, is whether chimpanzee and gorilla signing language; is it based on grammatical rules?
Chimpanzees cannot speak because, unlike homo sapiens, their vocal cords are located higher in their throats and cannot be controlled as delicately as human vocal cords.
It does not follow from their lack of speech, however, that chimpanzees are incapable of language. Perhaps they can acquire grammar like humans if they could only express it some other way.
The obvious alternative is sign language since all primates have extremely dexterous hands and sign language is a language. You have probably already read about the regular chimpanzees Washoe and NimChimpsky, and the lowland gorilla Koko, all of who learned to sign and interact very naturally with their trainers.
A simple way to disprove this hypothesis (the Innateness Hypothesis) is to demonstrate that other species have the capacity to speak but for some reason simply have not developed speech. A logical candidate for such a species is the chimpanzee, which shares 98.4% of the human genetic code.