This build will be fine for gaming. 1 better card would have been optimal to 2 low end cards. For example 2x7770s is like the same price as 1 7870 but the 7870 will perform better.
16gb of RAM is a waste for anything besides video encoding because games only use MAX 4gb. 8gb is the sweet spot for a gaming rig. also your RAM should be 1600mhz not 1333mhz. You won't really notice a difference but it cost the same.
Don't worry about your CPU. It will be fine for gaming.
Also, your PSU is of low quality and you might want to consider replacing it with a unit from Antec, XFX, Corsair, or Seasonic.