There is one key difference on your demo that I discovered right now. You have menus, sub and also sub sub menus, which all expand in your demo. But you do not have link targets behind the menu entries.
I would like to access the contact form on level one and the guestbook on level two.
I have a LG G Pad 8.3“ Android device with 1980×1080 px resolution. In portrait orientation, the menu switches to this other dropdown thing and everything works well.