the problem is laptop/hardware manufacturers RARELY produce what anyone in their right mind would consider a "gaming" laptop at that pricepoint. Oh sure there are laptops which can game fine in that price range, but the "gaming" laptops in that price range are almost universally junk.
This is the question i need to ask you, MUST you game in 1080p? Because if your answer is yes, i've got bad news. you're way under the budget you'll need to game in 1080p. If you don't mind gaming in 720p or 900p, then yes, there are laptops capable of gaming in those lowered resolutions in your price range.
here is the best "gaming" laptop i can find in your price range.
I highly suggest you add a SSD to it. it won't game in 1080p on serious top end games, but it should be fine at high graphic levels on less challanging titles, worse case you might need to scale down the resolution a little to play top end titles.
I'm actually surprised, this one is almost reasonable. usually "gaming" laptops are much worse collection of mismatched parts. if you can stretch the budget a little there is a version of that laptop with a 128gb SSD + the 1TB hard drive and an IPS screen. I would suggest that option. but it might be cheaper just to buy your own SSD and do the work yourself to set it up. your choice really.