Another update... I see that this is an intended feature for cleaning up the appearance on mobile devices. The issue is that it doesn't work if there's a submenu, because the overflow is hidden. Even making the overflow visible or scrollable, however, it's very clunky. So, I disabled the feature. However, the menu is now an issue on iPhone/iPad because, once you click the menu/submenu, it won't close.
Is there any chance that a redesign for the mobile menu is in the works? I love everything else about this theme, and think that this would make it perfect.
Note that I've looked at another person's website using this theme, and saw the same issue with submenus.