You should add and event handler for click events on dropdown-menu panel buttons, like this:
function showMenu(menuClass) {
var menu = $(menuClass);
$('#demo-container').bind("contextmenu", function (event) {
event.preventDefault();
menu.appendTo("body").css({
top: event.pageY + "px",
left: event.pageX + "px"
}).show();
})
}
$(document).ready(function(){
var page = $(this);
page.on("click",'.dropdown-menu button', function (event){
var button = $(this);
button.closest('.dropdown-menu').hide();
});
})