This would be a decent gaming laptop:
http://www.newegg.com/Product/Product.aspx?Item=N82E16834232574
At 1080P you should be able to play most games on high/ultra I think. Maybe medium/high on the most demanding stuff.
If you did decide to go for a portable desktop, this would give similar performance and can be overclocked:
PCPartPicker part list:
http://pcpartpicker.com/p/wBdBRB
Price breakdown by merchant: http://pcpartpicker.com/p/wBdBRB/by_merchant/
CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($64.99 @ NCIX US)
Motherboard: ASRock Z97M-ITX/AC Mini ITX LGA1150 Motherboard ($109.99 @ SuperBiiz)
Memory: Crucial Ballistix Sport 8GB (2 x 4GB) DDR3-1600 Memory ($44.49 @ Newegg)
Storage: PNY CS1111 240GB 2.5" Solid State Drive ($69.99 @ Micro Center)
Video Card: EVGA GeForce GTX 750 Ti 2GB Video Card ($122.98 @ Newegg)
Case: Lian-Li PC-TU100B Mini ITX Tower Case ($96.99 @ SuperBiiz)
Power Supply: Silverstone 300W 80+ Bronze Certified SFX Power Supply ($45.98 @ Newegg)
Total: $555.41
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-08-03 06:42 EDT-0400
You could bring the cost down a bit with a cheaper case and motherboard but it looks like the laptop is actually decent value as it is obviously more portable and includes a monitor and OS.