If you just mute it it should not mimize anything. Exactly what happens? And what are you playing?
If you put a full screen window up and then minimize that, you will see a Flash player icon in the task bar, is that what you are talking about? That is normal if you are playing a flash based video like off YouTube or something.
I just tried it on my two monitor setup, full screen YouTube, only time it goes back to windows is when I select a different browser tab. I clicked on another application on a different monitor, it brought up the taskbar, but when I clicked on the video, it just went to full screen again.
Is what you are clicking at another browser tab or window?