To stream music from my website, I highly recommend mpv, a minimal, versatile, FOSS media player. To stream an individual song, copy the link to it from the music page, then run
mpv [link], where
[link] is the link you copied. To stream a whole album, copy the "Stream" link for the album, then run
mpv --playlist=[link], where
[link] is again the link you copied.
You can also use VLC to stream individual songs. Simply copy the link to the song and paste it into VLC with Ctrl+V. I am not aware of a way to stream the full playlists with VLC, but if you find a way, please let me know!