How do I determine if MediaElement is playing?

What I did to "work around" that was subclass MediaPlayer (this would work for MediaElement as well) and add my own methods to Play/Pause/Stop. In those methods, I maintain a field which represents the playback status. Also, you need to hook MediaEnded so that you can change the status from 'playing' to 'stopped.'

You aren't missing anything. You pretty much have to manually keep track of whether or not the media is playing. It's a pity, since it is so easy in Silverlight, as you mention. Seems like a major oversight to me.

You can get at the _currentState member using reflection.

    private MediaState GetMediaState(MediaElement myMedia)
    {
        FieldInfo hlp = typeof(MediaElement).GetField("_helper", BindingFlags.NonPublic | BindingFlags.Instance);
        object helperObject = hlp.GetValue(myMedia);
        FieldInfo stateField = helperObject.GetType().GetField("_currentState", BindingFlags.NonPublic | BindingFlags.Instance);
        MediaState state = (MediaState)stateField.GetValue(helperObject);
        return state;
    }

This covers play/pause, but doesn't change from 'play' to 'stop' when it finishes.

You can get around this by adding an event handler to the MediaEnded event, and running the .Stop() method, this changes the status correctly (which can be picked up by the method above)