Alas, the world of Xfire and steam are a very different world from the rest of your software applications. I'm afraid you're probably not going to get very far without resorting to some kind of a dll.
Full screen games are a very specific thing. You might imagine that they would just be "on top" windows in the window hierarchy, which means you could just add another window "on top" of that game, and voila-- but this is not actually how these windows work. Full screen applications are special-- they are not part of the window hierarchy. In fact, the window hierarchy is completely disabled for the monitor when an application goes full screen, and Windows will give the application exclusive access to read/write directly to the monitor buffer as an optimization. So the full screen app isn't some borderless window that spans the full width/height of your monitor-- it literally *is* the entire monitor.
In other words, a full screen application is completely bypassing the Windows graphics layer when it renders data. This means that your GDI window isn't going to render, let alone be on top of the full screen game. The game has full draw access to the screen, and I'm afraid this means that Windows is not going to render any GDI data on that screen. In order to draw on that screen, you would have to do exactly what the game is doing, and draw directly to the monitor buffer-- but even then, the full screen app is likely to overwrite your data, so you will have to continually redraw your data every frame.
Steam and XFire solve this problem by writing very specific (and somewhat hacky) code for full screen applications. They are basically hooking directly into the DirectX/OpenGL drawing functions, catching calls to "DrawXXXX" and adding in their own overlays afterwards. You can read more about the process on this
StackOverflow page, which describes the method nicely. Like I said, it's messy, and even though you might think we're in the "age of Steam", this still isn't really a solved problem, technologically speaking. Programmers are still resorting to neanderthal tactics to hack these overlays into full screen apps, and it's not a trivial task.
So in short, I hate to say "give up", but unfortunately using mIRC script just won't cut it. If you know C/C++, take a look at the SO article and you might have better luck doing this natively. You definitely won't be able to use GDI as an overlay, though. You'll have to draw the entire overlay window manually.