Well at 1080p games will run at medium settings.Try to run games at 1650 x 900 resolution with vsync to off,AA to off then you can run games at med- high settings.
Try to tweak graphic settings in games to get more fps.
Will it handle moat games then but at a lower quality?
What is moat game?
With your cpu(tell us the exact model) you would enjoy games much more if you can get close to the $200 gpu range - HD7850 or GTX660 assuming your psu is up to the task. As you can tell, getting good advice is hard unless you give all your system specs. -Bruce