The article says so but I just tried to watch a video on iOS amazon video and it tells me to “Buy through the Amazon website or on your TV”. So I’m sure Spotify could say the same.
I believe it's about the type of product you're paying for -- the Spotify site specifically says Apple doesn't allow _content subscription_ services to be advertised through apps. In addition, I bet Prime gets away with it because it's not _purely_ a content subscription service.