Chromecast Audio by Google links the gap between your ordinary speaker and streaming services. It allows wireless music playback from any streaming app through Wi-Fi. While it supports Spotify, Deezer and the like, it doesn’t support Apple Music.
A report from Trusted Reviews gives a possible answer to why Apple Music is omitted. They asked a Google representative if the search giant asked Apple to join their roster, and Google certainly did. So the question now goes to Apple why are they not acting upon it.
The representative also said that Google has no barrier on any platform and they have an open SDK that any developer can use to support Chromecast.
Source: Trusted Reviews
Of course Apple won’t support Chromecast: they want you to use their own (and more expensive) AirPlay wireless connectivity system.