That still leaves you without an OS and the rather expensive controller. It's also the lovely US pricing. An RX 470 still runs you €200+ in Europe. Sure, you could shop around endlessly, but that way you're bound to run across a PS4 deal as well at some point. And why would you wanna build a PC like that in the first place. A couple of years ago a GTX 750 could go toe-to-toe with the PS4 as well. Now it's hopelessly outdated.
I included the OS price on my post, and my post is not trying to compare cent by cent, but to give the general idea that you don't need used parts (like on that video) to achieve that level of performance, trying to match prices is a little silly, but you can get a good gaming capable PC for prices not to far for consoles (and save money not paying for live/psn on the following years), that's it.
(also, I think there are ways to get Windows for less, for example I got it for free legally via the test program)
controller is optional on the PC, and there are hundreds of options, I still use my mouse and KB from the PS2 era actually (MS 1.1 keeps going forever), the 360 controller on the PC is still adequate if you prefer gamepads.
when the 750 ti was released the console gen was fairly new (and the specs were moderate for the 750, the big deal was power efficiency, not overall perf/price, the 7850 OC/R7 265/R7 370 was better at perf/$), so they had more to learn in terms of optimization than they have now I think, I don't expect the requirements for ports at console settings to grow much now, 470 should be safe playing ports better than PS4 until the end of its life... feels like the old gen a bit, from 2006 until perhaps 2008 having a PC to beat the consoles was a little pricey, after that it was really not a problem until the end of the gen, but it should be even less now given the hardware is less different or advanced on the consoles this gen.
yet the 750 ti is far from hopeless on every game out there, when you consider things like 30FPS cap, slow load times and CPUs specially, I can see a PC with a 750 Ti still doing better on some new titles.
also the 470 I mentioned is kind of overkill if you are trying just to beat the PS4, check the digital foundry video for Prey, the GTX 1050 non Ti with the Pentium delivers a far superior experience to any consoles, considering double the framerate + fast load times,
I want to add, cant seem to edit my posts, IGN did a head to head back in time, comparing Quake 3 on pc, ps2 and DC. IGN concluded that the PC sporting a voodoo3 had 'the best graphics of the lot'.
and you could achieve voodoo 3 levels of performance in 1998 on the PC (Voodoo 2 SLI), the rate of development was pretty amazing, a Geforce 2 GTS was already so far ahead of the V3, and I think they used a 30FPS cap on the PS2.
for those ports I think ram was critical, PS2 had so many ports with levels split and bad load times... in 2000 any gaming VGA would have at least 32MB at 2.7GB/s, with the GTS at over 5GB/s + the system ram (at least 128MB PC 133) and the hard drive, it was a huge disparity, like the TV vs Monitor back then.