I would say that ultimately, the i7-7700k can offer higher-performance in most existing games, and even if the 1600X's extra cores get better utilized by more games within the next couple years, the 7700k's clock speed advantage would likely prevent it from getting outperformed in most cases. Then again, it is a higher-priced processor, and the 1600X is competing more with i5s. If you're concerned about getting the highest frame-rates on a 165hz screen, and the higher price isn't a concern, then the 7700k seems like a reasonable choice, assuming you're also getting a graphics card that can push those kinds of frame-rates at the resolution and settings you want to play at.
Chugalug_ :
Ryzen is a good mix for streaming and gaming, but some people are still hyping themselves up choosing them over i5s and the like for simply gaming, while in reality the i5 7500 is far better optimized for DX11 and Open GL titles which nearly everything is running in, even for AMD cards DX12 is a step down in terms of performance.
From what I've seen, the Ryzen 5 series is right in line with the performance of the i5s that they're competing against, at least under more-common usage scenarios. Sure, in a number of recent DX11 titles, there may be a performance hit when running at lower-resolutions on higher-end graphics cards, but that typically only affects performance in the 100+fps range, where CPU performance can become the limiting factor, which doesn't apply to most people. Most will be playing these games on sub-100hz screens, or using graphics cards that can't push those kinds of frame-rates at their monitor's resolution, in which case any of these CPUs will perform virtually identically in most existing games.
And the i5-7500 is not "far better optimized for DX11". Existing games have simply not been optimized for Ryzen, since it's a new architecture. This brings up future performance, where the i5-7500 and 7600's four threads are likely to start impacting their performance eventually, as games continue to become more multithreaded. The i7-7700k at least has hyper-threading and higher core clocks that might afford it some more breathing room, but that's a $350 CPU, while the 1600X is only $250, placing it in a different price segment. And of course, now that Ryzen is available, developers can actually test their games on it, and optimize them for it while their games are in development, so it seems quite likely that relative performance will improve in upcoming games.