One site, all devices, is the general concept. Better marketing = better business. I understand your doubt's, but that figure is fairly accurate. Losing mobile traffic would be a big loss for gaining new users.

I agree on the desktop issue, it needs to support all sizes so this needs to be fixed and i'll change the menu to something better. But a button is still necessary for mobile navigation. I'll set all links to display in the top on larger screens and hide the button.