Mutter does not give focus to X11 apps which use an override-redirect Window for fullscreen mode
Mutter does not "see" X11 apps which use an override-redirect Window for fullscreen mode, they e.g. do not show up in the alt-tab list, and as such mutter also does not give them the keyboard focus.
Typically these kinda apps grab the X-keyboard, so they will still get key events as long as there is another X11 window, and that X11 window has the focus. But if there is no other X11 window, or the focus is on a mutter app, even if that mutter app is shown below the override-redirect Window (and thus not visible) then no kbd events are delivered to the app.
The app can also not be given the focus by using click-to focus and since it covers the entire screen, and not receiving input, it is also kinda hard to quit it again.