This is because of how X implementations treat multiple monitors differently compared to Windows.
X (at least implementations that I've used) by default has all monitors on one screen. When you go fullscreen, you change the screen size. If this is smaller than the screen with multiple monitors, extra monitors are disabled, because the screen no longer spans all of them.
In Windows, by default, each monitor has its own "screen". Unless you enable Nvidia surround/AMD equivalent/etc, which do what X does by default. If you enable that on Windows, you'll get the same behavior as you do on Linux.
This is why many games on Linux, for fullscreen, actually create a fullscreen window.
You could make each monitor have its own X screen, but, that's a user configuration choice, which an application cannot (and should not, imo) change.