It's pretty sad that they took Beats, which ran in the browser, and have somehow turned it into yet another piece of functionality bloating up the nearly intolerable iTunes. Well done Apple, well done!
And FWIW, a quick DDG search shows that people use WINE to run iTunes on Linux (though these results are several years old). So if you really want to try out Apple Music, it seems you can do so. But I wouldn't blame you for not wanting to go to that effort.
OTOH, they are going to provide an Android app in the fall. Maybe they'll provide something web-based as well.