But it says "on other music players". It doesn't really specify, but I would say that "Spotify" is the music player, and you still need to use it whether it is on the browser or other platform, but it is still "the same music player". I guess that the second case is more related to buying digital content, say an image, music, video, where you get the actual right to use that image, music, video on any platform. But I could be wrong.

In any case, as other users mentioned, if Apple music really lets ANY developer create an application that may reproduce the purchased content, then it may look fine.