That will work, thanks.
For games like those you listed, you're definitely going to need dedicated graphics if you want decent frame rates at decent graphical settings. I see you adjusted your budget too; with that budget, you can get a pretty good system. Check out the CX61 and GE60 from MSI; they're not beasts but certainly are capable.
Lenovo Y series is doing quite well also. Take a look at their Y400 and Y500 systems.
Clevo/Sager offers really good bang for the buck, but usually Windows is not bundled, so you would need to shell out extra for it. But, if you already have a valid copy of Windows, you can absolutely save yourself some cash by using that, and you'll probably end up with more bang for your buck from the system in that scenario.