The chosen UI for the like button is a double purpose control: it displays the current number of likes and likes the page when clicked.
However, there is no indication about what will happen when clicked. Upon hover (as seen in the screenshot), the hint does not mention anything about an action being performed upon click :
In addition, since the button does not follow the standard buttons style - seems completely rounded on the side, it's not obvious that it's a button and something will happen when clicked, the decoration could be just decoration. Thus, the only hint that an action will happen when the button will be clicked is the pointer cursor on it, and there is no information about what will happen.