Would this PC build work?

Solution
Should work with that CPU

1151 Core i7 i7-7700K(B0) Kaby Lake 4.2GHz BCLK 100MHz 8MB 91W All

Since it says all BIOS's support the CPU

The case says Mini-ITX/MicroATX/ATX and the mobo is MATX / which is micro ATX according to the site
No it wont work. You cant install an Intel CPU on an AMD mobo or vice versa

AMD and Intel CPU's / mobos are not compatible with each other

If you want an Intel system you need a socket 1151 / Kaby Lake mobo. Either B250 or Z270 mobo

And you cant install DDR 4 ram on that mobo