If I'm not mistaken, 'play on demand' in this context is a backronym[1]. The iPod name is apparently a reference to 2001: A Space Odyssey:
> The name came from a freelance copyrighter who, after seeing the prototype, thought of the movie 2001: A Space Odyssey and the phrase "Open the pod bay door, Hal!"[2]
> The name came from a freelance copyrighter who, after seeing the prototype, thought of the movie 2001: A Space Odyssey and the phrase "Open the pod bay door, Hal!"[2]
1: https://en.wikipedia.org/wiki/Backronym
2: https://www.pcmag.com/news/a-visual-history-of-apple-ipods