Yes, mIRC is the application in focus, on the left head usually, maximised, and the media player would be on the right head, fullscreen, playing a video file fullscreen (usually with DivX as the decoding filter). Clicking on the systray icon wont minimise mIRC under these conditions, instead mIRC seems to try to refocus itself.
The bug doesn't rear it's head with the video overlay inside the media player container window, only fullscreen.