Yeah, that is pretty much your best bet and you should grab it before Newegg decides to end the sale especially since they do not tell you when the sale ends. I think it has been on sale for at least a week by now.
You will likely have to play games at 1366x768 resolution at medium settings to get good performance in games since the 940m is only considered a good mainstream GPU not a gaming GPU. Actual performance will vary depending on the specific game.
Well the nVidia 940m is basically the best dedicated GPU you are going to get in the $500 price range considering that laptop is currently on sale. Otherwise, you are simply looking at laptops with integrated GPUs which will have much lower performance.
The nVidia GeForce GT 8600 is a desktop GPU from 2007. Most games list system requirements for desktops not laptops.
Yes the i5 5200u and 940m can play it smoothly I have the i5/2GB 940m/768 version of this laptop and it plays both of those games just fine. Jaguarskx is correct in that the optimal resolution for this GPU to play newer games at is 720/768 at medium settings. I'm not sure why they made a 4GB 940m as it's unlikely capable of utilizing the 4GB's especially at GDDR3 speed, my guess would be to either output to a 4K monitor/tv for movies, or if running a second monitor for multitasking, but even then. Either way jump on it, it won't last at the price.
It really depends on what you're trying to do. The consoles are ready to go, but games generally cost more and when the next system comes out your old games may not work on it. The real Gem in PC gaming is Steam, where you will pretty much have your games forever and they are usually cheaper or offer better deals than the consoles. But one thing you cannot get on a console is mods. Mods change the playing field of gaming in my opinion. You add what you like and it can greatly extend the life of a game. Most mods are free, and consoles just won't ever have them. If you took your $500 budget and applied it to a desktop PC instead of a laptop, the consoles don't stand a chance.