This loose assembly of used parts isn't a gaming pc. Running 5+ year old games at 30fps doesn't really count.
It's an 8 year old GPU that was fairly low end when new, and 4GB for RAM. That isn't meeting close to minimum requriements on most non-indie new releases. This is as much a "gaming PC" as a dusty used PS4.
In terms of CPU/GPU, my machine isn't much better than the one in the article yet runs plenty of games. I would be hard pressed to provide a list of games that I would want to play that won't run on it because: (a) most of the games that target high end rigs target a particular market segment and (b) there is an abundance of games that cross genres, art styles, etc. that target lower spec hardware. Chances are you're going to find something fun to play on low end hardware if you choose to explore your options rather than limit them.
(1050 TI: 6400 PassMark, 750 TI is 3800).
He's also well below the minimum CPU requirement.
A Xeon 1225 has a PassMark CPU score of 3,502. The minimum requirement for Doom Eternal is a 3.3Ghz i5, which, depending on which of the gazillions of i5 variants you mean, is a minimum of 5400.
If they really mean any 3.3Ghz i5, I say the Xeon E3-1225 is clearly superior to the i5-660 (dual core @ 3.3Ghz).
I really wish people would give real minimum specs again. Pick a specific processor you've run it on that it won't run on any worse and specify what cpu features you need, if any, so you know a higher end processor from previous generations won't work.
And right now, in the UK at least, console prices are mental. This would be cheaper than a PS4.
I am surprised they couldn't get anything better than a 750 for their budget. I think it's clear that at $100 you can still get a lot of bang for your buck by spending a bit more.