If you are experiencing a bottleneck, then should not be too bad when compared a more current generation Intel CPU. And there would only be a bottleneck if the game was dependent on the CPU, which most games are not.
Fallout 4 is an example of a game that is dependent on the CPU somewhat. From benchmark numbers I recall seeing yesterday, on ultra graphic settings @ 1080p using a GTX 980 Ti the performance difference between an i5-2500k and the i7-6700k both running at stock speed was 93 FPS vs 113 FPS. Sure there is a 20 FPS difference, but frame rates is still very good especially if you are only using a 60Hz LCD monitor which basically limits the FPS displayed on the screen to at most 60 FPS regardless if the GPU can push even higher FPS.
Skylake is Intel's current 6th generation Core i3/i5/i7 CPU. It will soon be replaced by 7th generation Kaby Lake CPUs which is basically just a refresh of the Skylake generation CPUs; not a totally new architecture. Intel has already confirmed that they started to ship Kaby Lake CPUs to system builders as of July 22nd. Therefore, 7th generation desktops and laptops should be available for sale relatively soon.
Since system builders gets first priority for new CPUs, it can take sometime other retailers (Amazon, Newegg, etc.) get those CPUs. And it may take a couple of months for prices to be equal to or less than Intel's MRSP for those CPUs due to high demand.