Would these specs make sense for a gaming PC?

How I would improve your build:

That specific Kingston ram is a bit on the expansive side, G.Skill has faster 2400MHz ram for less, and even Corsair has faster RAM for only a few dollars more.

The newer and faster 850 EVO and 850 PRO are actually cheaper than the 840 EVO right now...

The Z170-A is a bit on the expansive side, if you can pay that much for a motherboard, spend a little more for one of ASUS's Republic of Gamers motherboards instead.

Unless you specifically want to play games with Nvidia PhysX, the AMD RX480 has better performance for the same price. (assuming you can get your hands on one)

The Corsair CX500 and CX600 (both 80+ bronze) are currently cheaper than the EVGA 500B, alternatively, the Rosewill ARC M550, which is a 500w 80+ gold, is only a little more.

How I would build a 1000$ PC (link below)

i5 6400

Z170-E (allows for overclocking on a K series processor later on)

8GB of DDR4 2400MHz for 40$

Samsung 850 Pro + 1TB WD Blue

GTX1070 (assuming you can get your hands on one)

50$ case

Corsair CX500 for 30$

Windows 10

-The 6400 is more than enough for today's games, the GPU will be a more likely bottleneck than the CPU

-I'm not a big fan of higher cost Kingston stuff, that said, I do like their lower end stuff (eg laptop ram, affordable SSDs, etc), I would rather prefer Corsair RAM, which can take some overclocking abuse.

-I'm also a big fan of Corsair cases due to the easy cable management, that said, see if any of your local electronics stores has PC cases on display

-NOTE that you must use Windows 10 if you're using a Skylake CPU, you can google "Skylake Windows 10" for more details.

All I would upgrade the 960 to a 970 if possible, other than that it's decent

U can get better ones

Sounds respectable, however I would up the RAM to 16 GB if possible.