For just calling the functions:
Given your code, If you already have a btn_Quit_Clicked callback, just call ((Game*)Data)->GameExit(). (Where Data is the void * parameter to the function).
If you mean having the button call the quit function directly, see the follwing thread:
[Method pointer in define_key) (Deals with calling callbacks inside classes)
Hopefuly that answers your question - feel free to ask if you have more questions about it.