No, the window manager isn't in that chain. You can kill the window manager and your applications can keep running and drawing to the screen, but you can't move or resize windows. Also, instead of "Desktop environment" you mean GUI widget toolkit.
Gnome or KDE is just a package including a window manager and a bunch of mostly-standalone programs that give you a toolbar, file browser, settings panels, etc. It's not a layer that anything goes through. You don't even have to use the window manager it comes with.
> By desktop environment I meant e.g. Gnome or KDE. Aren't they separate from the widget toolkits?
I was being charitable. The desktop environment doesn't belong in the graph you drew. The GUI widgets belong in the place where you wrote "desktop environment". The charitable assumption is that you reasonably conflated the GUI widget toolkits for desktop environments, since the very popular KDE and Gnome are strongly tied to Qt and gtk, respectively.
No, the window manager isn't in that chain. You can kill the window manager and your applications can keep running and drawing to the screen, but you can't move or resize windows. Also, instead of "Desktop environment" you mean GUI widget toolkit.