Darren--

Microsoft also has an app., the icon for which is a pair of headphones.  When you move your pointer to the icon, "Music" comes on the screen.  The longer name for the app is Xbox Music.  That app will also play the .wma files.  Perhaps this app started with Windows 8.  

The Windows Media Player app icon has an equilateral triangle with the left side vertical, and on the right, a vertex of the triangle that seems to be pointing rightward.  It's the kind of triangle you see at websites inviting you to watch a video.  You click on that equilateral triangle that points rightward, and the video starts playing.  

In "Default Programs" within "Control Panel" you can make either Windows Media Player or Xbox Music the default app for .wma files in my Windows 8.1

F.H.