Here's the spec of that system as retail parts (case, keyboard and mouse just as examples) -
https://pcpartpicker.com/list/PTVq9J
Bear in mind those are retail prices, while the linked company probably gets their parts at a lot less. Now for $800, one might expect a slightly better system. Yes, I picked the named parts, and added cheap 1TB drive, cheap 2133 RAM, motherboard and so on, and so do many system builder companies. Also be aware that the RX 580 comes in both 4GB and 8GB flavours (handy for cutting costs when building and selling systems).
I respectfully advise you to look at a local system builder who is willing to give you an itemised build, rather than a website that over-prices on generic parts. Failing that, some companies do offer specified parts' builds, so you get to estimate if their prices are reasonable.
I got stung in 1997 for an over-priced PC, and started building my own thereafter. It's not for everyone, but there are plenty of people out there that could do it for you.
For what it's worth, here's a reasonable spec with the Ryzen 1600 and a more complementary setup
https://pcpartpicker.com/list/KyRpRJ
That includes a GTX 1060 6GB, a 250GB SSD for Windows 10, with a decent 1TB HDD for backup / games / files. The RAM is 2x4GB sticks of DDR4-2666 which is ideal for the Ryzen 1600 (the RAM comes in other colours, if that's important to you), and the case is an aesthetic choice, so each to their own. Just needs a keyboard and mouse of your own preference.
Compare your approximation of that 1400 system with my spec -
https://www.userbenchmark.com/PCBuilder/Custom/S0-M263821.268793.6753.43438vsS0-M258318.153864.413964.1767.90467?tab=CPU
Note that the 'gaming' score relates mostly to the gfx card. The system that has the RX580 is badly matched to a Ryzen 1400, so while the gaming benchmark score is good, in reality the CPU would struggle to get the most from it. The RX 580 (8GB model) and the GTX 1060 are very similar in performance, with the former having more RAM, and the latter being a little faster. Either would be fine with my 1600 system.
Best of luck with your PC endeavours.