Yes, of course the behavior would be different, as tapping is impossible with a mouse, and clicking is impossible with a finger. All the descriptions of the problem were from testing on the mobile devices I mentioned – a smartphone of unknown type, a Galaxy S5 using the default Android browser, and an Acer Iconia Tab A100 7″ Android tablet. The issue is with tapping, i.e. the use of a touchscreen. In those cases there is no such thing as hover, so the only way that a user can open the submenu is by tapping the parent item.
The only thing I did with my desktop browser was use it to confirm that your demo site had no link on the parent (I clicked and nothing happened). If your theme will not support a link on the parent item, you will need to make that very clear in your v. 2.5 documentation.