When I tried phones and tablets were positive for "any-pointer" (not good!). From my tests the most reliable way to check for a mouse/track point/track pad are

When I tried phones and tablets were positive for "any-pointer" (not good!). From my tests the most reliable way to check for a mouse/track point/track pad are (pointer: fine) and (not (hover: none). Personally, as a user, I don't like a menu that take the whole page when on a desktop, I find a top bar or a hamburger work much better, but those don't work with a small enough screen and without a pointer device (mobile devices), where a vertical menu with big buttons is more appropriate. But I'm not a UX specialist nor a designer, so this is what I suggest but obviously follow their specs.