I'm afraid using the normal wpf media player this can't be done.
The mediaplayer ignores the transparent regions, even with video formats that accept it. From memory, i dont think AVI files support transparent regions. MOV files do.
Having said that, and although it could be a very complicated task, it may be possible to enhance the WPFMediaKit mediaplayer to do what you want.
http://wpfmediakit.codeplex.com/
J Morrill the author of wpfmediakit may be able to let you know if it is possible or not.
I might add that i got around this problem in a project once by using a sequence of .png files that played a short 10 second movie. Of course this is not an ideal solution, but it got me out of a jam
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