I have no idea why you're against Dell. They're a really good company with really good customer support. They also have decent prices, at least if it you get it straight from them. Anyway.
A decent gaming laptop should have a good processor (3rd gen core i7 at least), a good amount of RAM (6GB or more) and a good graphics card (Depends on the game you want to play, but should be 2GB card or more).
That said, you're not going to find anything better than the Y580 in your price range, as I've said earlier.
Now IF you want a good set of processor, RAM and GPU, you're going to need to spend more. If you're willing to go to $1,200-$1,400, I could list out a million laptops for you to check out. If not, Lenovo and Dell are your best mates.
Asus's good stuff starts only after $1,200...