If it's for gaming,what's the point in a doubt? Of course the one with the better specs. Touch screens are useful when it comes to drawing some pictures using paint
or when playing angry birds the whole day. But if you intend to do some gaming,you got nothing to do with the touchscreens. Anyway,you're not gonna play games like FIFA or GTA without the keyboard and mouse but the touchscreen.
And,touch screens may prove to be useful only with some apps specially designed for such. Otherwise,they'll be having some drawbacks like screen getting coated with fingerprints,and hands getting tired. Though,it'll be good for some flicking of photos or doing such things.Since your aim is not that,but gaming,you'd best go for the one with better specs,the specs meaning better GPU,CPU and RAM.
And about the internet browsing,I'd say the mouse will prove to be better here as well,since you wouldn't want to take your hand near the screen everytime you want to scroll or shift through tabs. So,I'd say the other one without touch screen is best.