BadAsAl :
Even though they don't list the i7-6700K the one closest to it (at least when comparing passmark scores), the i7-4790K will still bottleneck the 1080 according to this site:
http://thebottlenecker.com/intel/1.html
In real world use will you still see bottlenecking? I don't know. I would guess the i7-6700K stock isn't that far from being ok with that GPU and maybe with a mild overclock it will not bottleneck.
Just as a side note that site is garbage. Whoever put that together doesn't know a thing about how this stuff works.
Upgrading a 4770 to a 6700k and expecting a huge gaming performance boost is an easy way to light hundreds of dollars on fire.
Lets go through the issues you're experiencing and what games they are in, as there is probably a solution to your problem that doesn't involve $500+ in new hardware.