Well, note that the use of CSS doesn't prevent the code of the mega menu from being provided to the viewer, the view is just then modified in this case to not display a section of the page. But, it is also important to first ensure that only that section is to be affected and that the page validates. For example, when I ran the page through an HTML validator, there are two errors associated with the html code, one of which is in the middle of what is identified as the megamenu-wrapper. The other is similar but before the wrapper.

Also, I loaded the page with my mobile device in both desktop and mobile mode and did receive two different results. There are ways to use php to simply not output the mega-menu code as can be seen/provided in includes/templates/responsive_classic/common/html_header.php.