while i agree that gaming laptops have a place, i'm not sure if the op is going to have budget for what you list. laptop hardware for what you get is expensive. a $800 pc in many cases is more than capable of trampling a $1500 laptop.
if you compare desktop and laptop parts of the same model the laptop models are inferior in performance. this is because they are designed for energy efficiency and heat efficiency.
lets take the gtx780 vs the gtx780m at BF4 @ ultra 1920x1080p
laptop: 40fps desktop: 67fps. also keep in mind that for the price you bought that laptop at you might be able to afford a 780ti for 81fps.
sources
http://www.notebookcheck.net/Battlefield-4-Benchmarked.105583.0.html http://www.anandtech.com/bench/product/1036?vs=1072
in this case the laptop is better suited for "high" not ultra while the desktop can play on "ultra" without issue. also due to the difference in performance the desktop will handle higher graphics settings for a longer period of time.
now, whether or not the desktop upgrade is a valid solution depends on two things: current hardware (is it even worth upgrading) and their own personal preferences (do they want to lug it to college and leave it there during the weekends).
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on a side note... ssd for the most part do not increase gaming performance, 32gb of ram is almost useless (normally 8 is fine) and 4-6 hours of use is not the battery life you would get during gaming sessions but during average non-gaming usage.
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i'm not saying that your idea for the op to get a gaming laptop is bad. i'm just listing a few points to consider which they might want to think about before going that route.