Menu is working fine it is just collapsed. Menu is shown when you tap the button, and it is very user friendly way for navigation to be shown on mobile.
Think about it, there are still vast amount of people who don’t have high resolution smartphones. What do you think, how vertical navigation will look like on those devices?
Theme is built with twitter bootstrap and if you go with that idea bootstrap should be recompiled - change breakpoint where Bootstrap menu becomes responsive. Check this post if you want to try. Also it is documented on bootstrap.
Regarding clicking one the main items instead of hoover. You should change file theme folder > js > scripts.js to your needs (clck instead of hover).