The performance of A10 IGP, namely HD 7660D, varies widely with the speed and performance of system Ram in use as it shares the system Ram for Graphics usage. Although the processing power of 7660D is same or little higher than HD 6670, even the cheaper version of 6670 comes with a dedicated high speed DDR3 memory, resulting better performance than 7660D with 1600 MHz system Ram. Unless you are using a 1866 MHz or 2133 MHz DDR3 memory with the A10, HD 6670 DDR3 performs better than 7660D. So for a dedicated Gaming system, Trinity setup is not advised and better to go with a Standard CPU + Good Graphics card combination.
Also, G645 is capable enough to handle GPU up to GTX 650 TI without any bottleneck and it will easily handle HD 7770. As your need is gaming, go with G645 + HD 7770 combination.