I would guess a lot of games do not 'listen' for a click event, but watch for the LMB to be clicked (since that usually can be remapped somewhere else.)
The difference:
When you click on the desktop for instance, 2 things are fired: 1- That the button on your mouse has been pressed, and then Windows knows to take that button press and interpret it as 'you clicked on the thing that is under your cursor' (referred as the click event).
I can say that because when I used to do flash programming, you could call upon a click event by two ways: onClick and onKeyEvent('keycode'). (The functions could be wrong, it was 15 years ago. But its just to show there was 2 ways to listen that there was a click of the mouse.)
I would imagine that the 'doubleclick' function of the mouse basically doesn't say 'the LMB has been pressed twice quickly' but is more 'fire the click event twice'. And that would be why, in a game where you can remap LMB somewhere else, that button is dead. Because its listening to the button being pressed, and not the click event.
I can't seem to find a good way to test which of the 2 have been fired. But that would confirm/disprove my theory.