How well will this computer run games AMD Phenom II X6 1090T Black Edition 3.2GHz Socket AM3 Desktop Processor Kingston HyperX 16GB DDR3 Memory Sapphire AMD Radeon HD 6970 2GB 256-Bit GDDR5 PCI Expres

This computer should be able to play "anything" on the market. However there are some very well known issues with games having excessive lagging on computers with Radeon, such as "Watch_Dogs". This is an issue with the games themselves (an awful port from console to PC), not the computer.