Webform Radio buttons are not getting "radio-checked" class when clicked on
After a bit more digging, it appears it's my memory that has failed me. This functionality is provided by Javascript.
So I'm placing my solution here in case anyone would like to make their select options look like buttons.

You have my CSS above.  Next you need to add a javascript folder &amp; file in your sites> all >themes > [theme_name] directory. 

I've placed a new folder and file in the above path :  js > webform_tweaks.js

Inside the webform_tweaks.js file, place this code:

(function($) {
  // DOM ready
  $(function(){
    // add a radio-checked additional CSS class to the parent label
    $(".webform-client-form .form-radios input").click(function(){
      $(this.parentNode.parentNode.parentNode).find('.form-item .control-label').removeClass('radio-checked');
      $(this.parentNode).addClass('radio-checked');
    });
  });
})(jQuery);  

You need to reference this javascript file in your [theme_name].info file (found in the root of your sites> all >themes > [theme_name] directory.)

Open that file and add: 

scripts[] = js/webform_tweaks.js


You will also need to flush your CSS &amp; Javascript caches before you see the change. 

Hopefully, now you should be able to click on your "pretend" button and apply a style to it using this new "radio-checked" class and make the button looked clicked by adding a background colour or something to it.