jQuery objects do not have a classList
property. To use classList, you must extract the element from the jquery object.
$('.page').get(0).classList.contains('story')
however, you can simplify this by using jquery's .is
method or .hasClass
method.
$('.page').is('.story'); // true/false
$('.page').hasClass('story'); // true/false
or even:
$(".page.story").length; // 0/n
Additionally, if you wanted the result of this conditional to happen after the .load has completed, you must move it inside the .load callback after your animation line.
$('.content_loading_container').load('content/'+fileName, function(){
$('.content_wrapper').delay(250).animate({opacity:1}, 500);
if ($('.page').hasClass('story')) {
...
});