jQuery - exclusive input checkboxes - enable to uncheck by clicking on current checked input

I did an exclusive menu of 2 input checkboxes on the following link :

exclusive checkboxes

As you can see, each input checkbox corresponds to a different case : (Player Vs Computer) and (Player1 Vs Player2) and each case is associated to 2 buttons (which work as I want).

My issue is that I would like to add a functionality, i.e enable to uncheck the current checkhed box by clicking on the current checkbox (this one which is already checked).

For the moment, I have to click directly on the other input checkbox to uncheck the current one; I would like to get the both functionalities.

Here's the current code which handles these 2 exclusive input checkbox :

// Check input checked
 checkBoxState = $('#'+gameType+'').find('.game').prop('checked');
// Set oneButtonClicked to no for restore
 $('#formGame').prop('oneButtonClicked', 'no');
 // Handling input.game
 $('#'+gameType+'').find('.game').prop('checked', !checkBoxState);
 //$('#'+gameType+'').siblings().find('.game').prop('checked', checkBoxState);
 // Set pointer-events to all for formGame
 $('#formGame').css('pointer-events', 'all');
 // Handling button.btn
 $('#'+gameType+'').find('.btn').css('pointer-events', 'none');
 $('#'+gameType+'').siblings().find('.btn').css('pointer-events', 'all');
 $('#'+gameType+'').find('.btn').prop('disabled', checkBoxState);
 $('#'+gameType+'').siblings().find('.btn').prop('disabled', !checkBoxState);

gameType is the current type of game (Player Vs Computer or Player1 Vs Player2).

input.game represent the input checkboxes

button.btnrepresent the 2 buttons available for each ìnput.game.

If someone could tell me how to add this functionality, i.e unchek by clicking on current checked ,or unchek by clicking directly on the other checkbox ...

Feel free to ask me further informations about this issue.

Thanks in advance