ja, it looks ok for a budget build, but i would use an i5, as the i3 will slightly bottleneck the 6870... but if ur dead set on it, then it could play these games on 1080, but not on a high AA...if any.
p67 is unnecessary for a non k series as they cannot overclock. Look for a h61/67 it will save you some money. 750w is pretty overkill for a single 6870, not to mention thermaltake is not exactly the best psu manufacturer out there. You can save some money by switching this to something like the corsair cx500.
As far as the i3 bottle-necking the 6870, no it won't the i3 is a very capable gaming chip that can deliver higher performance than a stock 955be.