As long as the desktop environment provides a mechanism for applications to register their global shortcuts then all is well. However, without such a feature the application has to just listen for all keystrokes and check if it matches something the user's configured.

Example: I've bound several scenes in OBS to keyboard shortcuts so that I can switch scenes no matter what application I'm in. I'm pretty sure OBS does this by listening to all keyboard events on the root window. It's not very efficient, but it works.

Now imagine having to support a global shortcut daemon per DE that exists. I suppose someone would write an abstraction but really, it's something that FreeDesktop.org should provide (if it already doesn't).