The thousand-songs-in-your-pocket sales pitch was more than lifestyle/concept -- it was an actual feature. All of the other players at the time were big & bulky because the components they used for storage & battery required the corresponding form factor. The "pocket" part of the sales pitch was exactly that: the ipod physically fit in your pocket because the components were smaller and more integrated. In the stage demoes by Jobs, he shoves the ipod into his jeans.
To the author's point about "you pay for the problem it solves, or the needs/wants it fulfills", the implied need here was that you need this to be small and out-of-the-way -- not a miniature home-stereo attached to your belt.
And not to pick on the author, but I don't find the ipod reference very applicable to the case of communicating with your consulting clients. Sure, you have to speak to your audience -- but direct 1:1 contact with a handful of stakeholders is hella different from millions of consumers who never asked you for a specific set of features and a timeline.