About the 4th PC that you linked.
By default, it is better in games than the i5-6600K build but only because it has the GTX 1060 6GB GPU in it.
If it had the same GTX 1050 GPU as the i5-6600K build has, it would be far worse than i5-6600K build.
Here you have a decision to make. Either go with the 4th build, that has FX-6300 CPU, GTX 1060 6GB GPU, 2x 8GB DDR3 RAM at 1600 Mhz, 120GB SSD and 1TB HDD.
Do note that only CPU upgrade would be FX-8350 but it doesn't come even close to the performance of i5-6600K.
Or go with the 2nd build with i5-6600K CPU, GTX 1050 GPU, 2x 4GB DDR4 RAM at 3000 Mhz and 1TB HDD.
Just swap out the GPU and you have a solid high-end gaming rig according to the today's standards. You can even OC (overclock) the i5-6600K to reach the levels of i7-6700 if you so desire.
My suggestion would be that you go with the i5-6600K build.
I have 3 PCs in my household, Skylake, Haswell and AMD. Specs in my signature. There's a reason why i don't use AMD FX CPUs in my PCs.
Even though AMD FX series CPUs have more cores and threads than the Intel counterpart, it is also outdated technology (released in 2012), compared to the Intel's Skylake family (released in 2015).
AMD FX CPUs are more for a video rendering and server environment than for gaming.
A comparison between FX-6300 and i5-6600K,
link:
http://cpu.userbenchmark.com/Compare/AMD-FX-6300-vs-Intel-Core-i5-6600K/1555vs3503
Also a comparison between FX-8350 and i5-6600K,
link:
http://cpu.userbenchmark.com/Compare/AMD-FX-8350-vs-Intel-Core-i5-6600K/1489vs3503
And for bonus, a comparison between FX-8350 and i3-6100,
link:
http://cpu.userbenchmark.com/Compare/AMD-FX-8350-vs-Intel-Core-i3-6100/1489vs3511
Do note that i3-6100 is considered as entry level/ low-end CPU according to the today's standards.