Are you sure that the laptop has a desktop gpu? I personally would get barebone laptops at this price range as you should be able to get a gtx 980m or an sli.
Help me choose between Alienware 15 with i5 processor and gtx 970 and suggest good gaming laptop under 1350 $
Are you sure you wish to go with a laptop? Gaming laptops are quite heavy and arduous to carry. Not to mention you must carry a mouse(for those fps games) and the adapter with you too! $1350 can get you a pretty good desktop.
As for the Alienware. Buy one with an i7. The GTX 970 is the mobile chip and is quite slower than its desktop counterpart. Not really recommended for 1080p gaming.