Right, I am able to reproduce this now.
Clicking on the mIRC tray icon performs three functions (as opposed to two functions like other applications): 1) if mIRC is the topmost window, mIRC is minimized to tray, 2) if mIRC is already minimized to tray, it is made visible, 3) if mIRC is visible but not the topmost window, it is made the topmost window.
It looks like the issue is with the 3rd feature. Because the media player is fullscreen, it places itself as the topmost window, which mIRC can't override. I'm not sure if there's an easy solution to this other than removing support for the 3rd feature, I am looking into it.
Update: I've added multi-monitor support to the tray click feature which appears to resolve the issue, so this should be fixed in the next version.