If I'm reading your post correctly, you are downloading purchased music from Music Match, however, the files are WMA files.  Is this correct, so far?  I have Music Match Jukebox Pro V8 (paid version) and it will play WMA files, but as you have found out will not convert WMA files to some other format.

However, the Digital Rights for purchased downoladed songs from the internet varies with the site you are purchasing them from.  Some have digital rights that you can only play the songs on their player (e.g. MusicMatch Jukebox) but cannot do anything (legally) with the music such as burn a music CD, etc.  Other pay music services will allow you to do other things, e.g. iTunes will allow you to burn a CD of songs you download from them, however, you have to use the ITunes player BUT, the iTunes player does not support many CD burners so there is a limit there.  Each pay music download service has their own "fine print" rules and you will have to read the "fine print" to determine what you can or can't do (legally) with their music.

I am assuming you are using Windows XP.  Musicmatch came with the Windows program.  Have you e-mailed Music match at:  custsup@musicmatch.com?  When downloading, the music purchased goes into "My Library" and to "Playlist".  From there, the music can be recorded to a disc.  BTW, I am using Musicmatch Plus 8.2.  Check that out too.