Same here. I've never had an Xbox.. (PC gamer here!) in fact, the last game console I owned was a Super Nintendo if that tells you anything. I have been a gamer though.. on the PC since way back in the DOS days.
Nope, you're not missing anything. Except for an awkward service that tries to lure you into signing up for an "Xbox Music Pass" for $9.99 a month to be able to stream music (that you already own) to all your devices. I guess if one has an Xbox, it has it's perks though. A lot of Xbox users (360 and One) have purchased tons of music through the Xbox music service over the years, so the service and it's consumer base/ecosystem isn't going anywhere... kinda like iTunes and it's customer base; People have a bunch of money and time invested in their iTunes music collections. It makes sense that the Xbox music users want these apps, and want it to be an integrated part of Windows Phone (if only they could work out the kinks I hear), but that doesn't mean WE have to use it. There's always been other methods of obtaining music...
Some of us Windows Phone 8(8.1) users have huge collections of music that we'd like to listen to every now and then... Without getting involved in all that Xbox Music business.... thank god for Nokia Mix Radio!
Nokia Mix Radio (formerly Nokia Music) on the other hand is awesome! With NMR, you can play all your local music (mp3 files on your phone) and you can also create artist "mixes". By entering up to three artists, NMR will play music from your favorites and similar artists (think Pandora or iHeart radio) or for even more diverse mixes, you can have it do a "computer scan" on your PC, and let it find all your music files/folders and it'll generate mixes (which are downloadable for offline play) based on your entire collection.
The only thing I've been worried about really, is the Microsoft/Nokia acquisition, and what happens to Nokia Mix Radio. I really hope we get to keep it... Because with Microsoft and their pushing Xbox music, NMR's days may be numbered...
Oh and sorry for the long post (I'm highly caffeinated!) and I don't mean to hijack the op's thread... Just seemed relevant to me.
Long live NMR!!!