How did this site "manipulate" the mouse position?

The most plausible answer to how the site did this is to use Keyword values, more precisely the "none"

  

cursor: none;

In this way he can "hide" the cursor but it remains in place, if you right click for example (would be an excellent test) could identify the exact location of the cursor, just above the exact location of the cursor your cursor it would add an image "out of the alert" of a cursor thus deceiving anyone who had tried to click to leave, but again I remember that if you click even without seeing the cursor would work, currently or in the future I think it is possible to manipulate the mouse cursor with javascript except with an extension installed directly in the browser or something.

<div style="cursor:none;">Teste cursor</div>