The whole point of TFA is that this may well not be the case. It may well be the case that language is not the product of hard wired wetware, sometimes known as "the Language Instinct," but is rather the product of:
1. general symbolic intelligence, i.e., thought, coupled with:
2. the ability to make more complex sounds, due to a vocal tract modified from anthropoid ape ancestors by the shift of the relative positions of neck and head brought on by bipedalism, and:
3. cultural transmission, i.e., the ability to pass language on to the next generation due to the long childhood dependency of humans which, in turn, came about because our large heads won't fit through the birth canal at full size, so we are all effectively born premature - unable to walk, or even effectively grasp our mother's hair and cling to her.
Therefore, it is quite possible that once our ancestors developed sufficiently large and complex brains to think with more logical sophistication than, for example chimpanzees, we slowly over time dveloped more and more complex languages until we reached a plateau, specifically, the limit of children under the age of 6 or 7 to understand and learn the basic grammar and vocabulary of the language.
Any increased grammatical complexity beyond this point would immediately die out since the next generation could not learn it during childhood. Once this plateau was reached, presumably in southern Africa ca. 200,000 years ago, our ancestors had the cognitive "killer app," i.e., modern human language, that allowed them to successfully radiate across the planet.