Yes, they claim their voice reco "really works" - I don't find it a credible claim... except that, when you have a confined univese of possible matches (e.g. grocery items), it doesn't so much have to recognise the word, as distinguish between the known candidates. For example, just counting the number of syllables can narrows it down (even identif it: yif expecting a digit, only "7" has two). And no verbs etc.

Isn't the scanner online (so it can tell amazon what you ordered)? If so, I expect it uses servers, like siri and google voice. (Also processors are pretty small these days: the CPU in a phone takes up dramatically less space than the display or battery).

They can back the voice recognition with mechanical Turk. If the recognizer has a lower confidence than desired they just ship the sample to a human.