As I said before, the escape key is used universally to get the menu screen. And I doubt it's able to be rebound. Any other key, yes, as the prompt you just spoke of won't interfere with rebinding any other key. From the prompt you are seeing, you can't rebind it. Sorry.
probably you don't need this anymore but there is a way to do it: while BF4 is not running simply edit file "Documents\Battlefield 4\settings\PROFSAVE_profile" and search for properties ending with ".button", these can accept an int argument and 1 here represents the ESC key, simple as that. Make sure within every category (infantry, heli, etc..) all value are unique so no binding used twice.
