Earlier quoted context omitted.
That's mixing the medium and the content to me like how Art Deco isn't just architecture it's a style.
If they broadcast them over radio, is it still a podcast? Emailed out the audio files to a mailing list? Distributed them on cassette tape? It seems to me the format is part of it. RSS or something equivalent (Atom), feeding audio files to whatever client you bring, is a podcast. Youtube videos aren't podcasts just because I listen to them in the background (though one might also have a youtube video of one's podcast…
Personally I'm not a fan of Spotify locking down podcasts because I do like that I can use whatever app I like but I'm not going to call something not a podcast because it's annoying to get.