A few things:
"Gaming Laptop" is a misnomer. Mobility isn't something you should consider when buying a device to run video games on. You aren't so dependent that you need to play this game on the go, trust me. The more apt the device is to be able to run the game, the less mobile it is becoming because the overall size, weight, and heat output are going to increase significantly.
Apple products are going to be significantly more expensive than pretty much anything else you can buy, and are not made with gaming in mind to begin with. That isn't their niche. Most people "need" Apple products for their design suites or because they don't know any better. Stick to PC stuff, especially if you are trying to stick to a budget.
Given your requirements, it makes me feel like you are probably trying to buy this laptop to be an all-in-one device that you need for school, possibly business. You're now skimping on the things that are necessary to effectively get your settings high for the convenience or perception therein of the mobility you feel you need. I have met very few people in my life that needed anything more than a smartphone or a $250 chromebook for the things they do when mobile. If you're mobile requirements amount to "Internet and Facebook" like 97% of users, then stick with the options I just mentioned.
for $800, you can buy a Desktop that would chomp the requirements for League of Legends worse than getting Cho'Gath picked into Teemo. Heck, for $600, you could buy one that would be able to run the game on generally High setting and have $200 to buy a mobile solution like I mentioned before.
Logicalincrements.com is your best friend when looking to buy. And I cannot recommend you purchase anything except a desktop when you list "gaming" as a primary function.