I made a few revisions. Better cpu and motherboard and I doubled your hard drive for basically the same exact price.
Honestly, this is not as bad as people will try to have you believe. This will game @ 720p pretty well, but if you are shooting for 1080p, then this is not for you, BUT $334 is not going to get you a 1080p gaming system anyway so....
PCPartPicker part list:
http://pcpartpicker.com/p/3hMor
Price breakdown by merchant: http://pcpartpicker.com/p/3hMor/by_merchant/
Benchmarks: http://pcpartpicker.com/p/3hMor/benchmarks/
CPU: AMD A10-6790K 4.0GHz Quad-Core Processor ($109.99 @ NCIX US)
Motherboard: Gigabyte GA-F2A75M-HD2 Micro ATX FM2+ Motherboard ($54.99 @ Newegg)
Memory: G.Skill Ripjaws X Series 4GB (2 x 2GB) DDR3-1866 Memory ($49.99 @ Newegg)
Storage: Hitachi Ultrastar 1TB 3.5" 7200RPM Internal Hard Drive ($52.00 @ Amazon)
Case: Xion XON-560 MicroATX Mini Tower Case ($34.98 @ Newegg)
Power Supply: Corsair Builder 430W 80+ Bronze Certified ATX Power Supply ($19.99 @ Newegg)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($15.99 @ Micro Center)
Total: $337.93
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2014-03-28 00:38 EDT-0400)