GNOME's GTK Vulkan Renderer Faster Than OpenGL, Now Working On Windows

[ebassi]

embassi, is there any chance for a game engine to use gtk to save time when implementing a GUI library?

Not really.

The whole rendering pipeline for GTK is optimised for the GTK use case — widgets, text, icons. At most, GTK can provide you with an escape hatch, and give you a widget where you render with OpenGL, and then the toolkit will upload the contents to the GPU alongside the rest of the UI. You could create a game level editor; or write a CAD application; or a preview for GLSL shaders — but the display bit would still require you to write your own game engine.