Question, the short version:

I want to be able to detect if any X application is running in "fullscreen mode". Not if the window is maximized, but if the application is overriding/bypassing the window manager. Like, for example, a game or a media player in fullscreen mode.

Why do I want to do this?

I hate it when I'm watching a movie on the computer and the screensaver kicks in and I have to either futz with the mouse/keyboard or kill the screensaver engine. I'd rather run a script periodically to check if certain applications are running in fullscreen mode, and if they are, kill the screensaver engine until the programs are no longer running in fullscreen mode.

Would this be a function of X or a function of the windowing manager?

Any input would be appreciated.

I regularly use kaffeine for this purpose (viewing films full-screen). It has the ability to prevent the screensaver from activating while you are watching a film. It is clever enough to allow reactivate the screensaver if you've paused the film. You might look into how they do it. It is clear that what you want can be done.
cheers,
jdk