Unfortunately there is no hide method on the tabs plugin. With the option method you are only changing the setting of the plugin. You have to trigger the click event on the active tab like this:
$(".btn-close").on( "click", function() {
$("#tabs").find('li.ui-state-active a').trigger('click');
});
(This answer uses the improvements suggested by A.Wolff to remove the dependency to the parent element.)
Here your updated fiddle