There is no "quick exit" button.

There's q, or ctrl+q, both of which bring up a prompt to exit the game, which you need to confirm.

There's also Esc, which does the same as Q and Ctrl+Q, so it also asks for confirmation. Then there are ways to close windows that are native to Windows, such as Alt+F4 or Alt+Space followed by C (or whatever the menu item "Close" is bound to in your installation; essentially the same as Alt+F4, but this doesn't work in TPT becuase our UI eats keydown events from Space), which will immediately close the window without a confirm prompt. I believe that this behaviour is what the Fast Quit option in the options dialog should moderate, but as far as I can tell, it currently doesn't. Nope, it's apparently not.

 

But yeah, no other hidden shortcuts like 5 or 4.