No.
There is NO valid correlation between screen dimensions and touch
capability. None. Zero. Zilch. Nada.
Too many devices, too many screen sizes.
And it's a bad assumption in any case. User might have a
bluetooth mouse, for example.
If you want to know if the device supports touch, check if it
supports touch. Google about how, because there are various ways
depending on the browser. The easy, reliable way is to use Modernizr.
That it supports touch doesn't mean that the user uses touch.
They might use a mouse.
Only thing you can know for sure is if it does not support touch.
As I suppose you have found out, hover is a horrible experience on
a touchscreen.
IMO, it's equally horrible with a mouse. But that is a matter
of opinion. Especially bad are "Microsoft"-style flyout
menus, that require that you manipulate the mouse path carefully, else
the first-level menu disappears before you carefully navigate over to
a submenu.
(I see though you are using a horizontal top level and vertical
second level, which does work out very nicely on desktop. Congrats on
avoiding the flyout trap!)
I suggest you see if touch is supported. If it is not, then use
your hover version. If it is supported, use the click version. You
will I suppose make some users that have devices that can do both
unhappy. (Or maybe happy, depending on their point of view.)
