You can subscribe to the PlayStateChange event of the player.
wmp.PlayStateChange += new AxWMPLib._WMPOCXEvents_PlayStateChangeEventHandler(wmp_PlayStateChange);
private void wmp_PlayStateChange(object sender, AxWMPLib._WMPOCXEvents_PlayStateChangeEvent e)
{
if(e.newState == 8)
this.Close();
}