The big difference here is that a backprop model needs to essentially be told what the correct phonemic boundaries are, etc., either in the way it represents the phonemes (possibly as a localist representation) or as target outputs. The model discussed in PNAS is simply given raw speech sounds and learns the categories itself (and how many there are) with no given targets. It's the difference between an unsupervised and supervised model that makes the difference here. In the earliest stages of language learning, I don't think parents correct their children's babbling!

It is terribly ironic that someone from MIT would claim that the brain operating continuously was a longstanding and obvious overriding assumption. MIT (historically their AI lab, and more recently their Brain & Cognitive Sciences Department and their Linguistics Department) is where much of the fervor and argumentation for the mind being a finite state automaton came from. Personally, I couldn't agree more that neurophysiological data make it obvious that the brain functions essentially continuously, but if you read a contemporary cognitive psychology textbook you'll see a very different "information-processing approach" as the dominant perspective.