Is this good gaming and 1080p video editing rig?

Solution
4 threads only for video editing is not good enough
spend too much on the video card
16 gb is recommended for video editing, 8 gb is kind of small due to windows occupying a good chunk already
also video editing on HDD? Add a normal SSD at least
case is not recommended, rosewill is not good quality
psu is no good

What is your max budget?

If I were you, I will get this:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD - Ryzen 5 1400 3.2GHz Quad-Core Processor ($154.99 @ Amazon)
Motherboard: ASRock - AB350 Pro4 ATX AM4 Motherboard ($87.99 @ SuperBiiz)
Memory: G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-3200 Memory ($191.99 @ Newegg)
Storage:...


That's not bad. Assuming the program supports hardware acceleration, the GPU will help out quite a bit when rendering.
 
4 threads only for video editing is not good enough
spend too much on the video card
16 gb is recommended for video editing, 8 gb is kind of small due to windows occupying a good chunk already
also video editing on HDD? Add a normal SSD at least
case is not recommended, rosewill is not good quality
psu is no good

What is your max budget?

If I were you, I will get this:

PCPartPicker part list / Price breakdown by merchant

CPU: AMD - Ryzen 5 1400 3.2GHz Quad-Core Processor ($154.99 @ Amazon)
Motherboard: ASRock - AB350 Pro4 ATX AM4 Motherboard ($87.99 @ SuperBiiz)
Memory: G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-3200 Memory ($191.99 @ Newegg)
Storage: Samsung - 960 EVO 250GB M.2-2280 Solid State Drive ($120.89 @ OutletPC)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($46.69 @ OutletPC)
Video Card: Gigabyte - GeForce GTX 1060 6GB 6GB G1 Gaming Video Card ($336.17 @ PCM)
Case: Corsair - 270R ATX Mid Tower Case ($54.99 @ Newegg)
Power Supply: Corsair - TXM Gold 550W 80+ Gold Certified Semi-Modular ATX Power Supply ($64.99 @ Newegg)
Total: $1058.70
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-01-14 11:37 EST-0500

8 threads will be better for video editing, OCed 1400 is on par or better in gaming, 16 gb very good to have. nvme ssd video editing is best
 
Solution
Exactly what vapour said. Though, a Core i3 quad core would work decently fine for video editing, however a Ryzen 5 with a B350 motherboard is a far better bargin and is quite a bit faster for video encoding and rendering.

The only thing I'd change from Vapour's build is going for a SATA based Samusng 850 EVO 500GB drive for just a tad more.
 

unspeakable

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That i3 is not enough for any video editing, since it's a dual core, with four threads. Core i7 are a bit pricy so you are open to the Ryzen world. A Ryzen 5 1400 (stated above by vapour) is the best bet, and fits best into your budget if you buy a $70 B350 motherboard.
https://www.newegg.com/Product/Product.aspx?Item=N82E16813144048&cm_re=AM4_B350-_-13-144-048-_-Product
That's my favorite AM4 MOBO, otherwise a cheap $100 mini ITX works too.
If you are using wifi than a cheap $100 MiniITX is the way to go, because then you don't have to use crappy USB wifi adapters, or buy a wifi card.

 


Just an FYI, OP listed a Coffee Lake i3 in his build which is a quad core.