If you purchased them through the Play Store they will only be available through the Play Music app. You can download them for offline use (There should be an OFFLINE button in each album) but they can still only be played through that app.
I do believe there are apps that let you access your Google Play music, but I might be wrong or they might require some form of trickery/hackery/root. In any case, Play Music is not such a bad app. And you can always play the albums online from any browser, so that's cool. You can also upload your own music files into Google's servers and have your own library streamable from any device.
I thought if you purchased the track/album outright, you could play it anywhere. But if you download it with an All Access subscription, it can only play in the Play Music app, as long as your subscription is current.