I set my Tribler-preferences so that Tribler closes tot the systemtray next to the clock. When I just played a video with the on-board videoplayer, and I minimize Tribler, the program will go to the systemtray but the videoplayer is still visible in the taskbar next to the start-button. I think the videoplayer should go to the systemtray as well whn it's opened and someone minimizes Tribler. I run Tribler on Vista so I don't know if this is the same under XP as well.
Good Luck
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Described problem also occurs under XP.