There's no Ajax involved in Heise's thing.
The Facebook like button is not directly put into the webpage, because that could cause issues with the cross-origin policy in browsers (a browser lets only pages on facebook.com to make Ajax requests to facebook.com).
Instead, the like button is in an iframe, which is a different webpage stored in a frame in another webpage. Those don't require any sort of Ajax at all. Instead, clicking the gray icon uses JavaScript (which is definitely NOT Ajax) to replace their grayed-out like button with an iframe containing the actual one.
FTR, in case you didn't guess already, the iframe points to a webpage on facebook.com that contains the webpage for the like button.