I agree with your general sentiment regarding making advanced topics accessible. But since you proof-read the article, I hope you are not suggesting that knowledge of Hadamard gates should be considered as "accessible."
In any case, the main reason why I think of this article as "popular science" is because it fails to even attempt to explain quantum fourier transforms in layman's terms. The author even admits that such an explanation is beyond the scope of the article and instead uses the analogy of audio signal processing to draw an analogy between audio signals and QFT, hand-waving at some connection between the two solely by virtue of the fact that both use Fourier transforms. I am sorry, but I have seen this cliche way too many times--that quantum physics and music/audio are somehow intertwined and can be used as analogies for each other, just because of the fact that both can be described as waves? In the end, the most essential part is left unexplained, and only a vague analogy with a more familiar system (audio) is drawn, leaving only an imprint of false understanding. Popular science.
Since QFT is a prerequisite for quantum factoring, in my opinion this article does not explain a thing. Sure, people may become more interested in QI after reading this article, but in that case, let's be honest about what this article is: an advertisement, not an explanation. Show me a macroscopic system that exhibits true wave-particle duality and can be used as an analogy for quantum systems, then I'll take it seriously.