I have the 1E DMG secondhand, so I know in theory. That's what It saying, they aren't recreating the 1E rules, but a feeling (per their stated intent in the text). Most players won't have any familiarity with 1E.
They don't feel remotely like 1E, though, that's the thing.
1E's vibe was that psionics were this really random and potentially powerful thing, but which was secondary to the abilities of other classes (even though sometimes it was actually way more powerful than them, confusingly). Even the Wild Talent thing here doesn't much resemble the 1E implementation. The comment that they were like 1E solely related to the "not an actual class you can pick" point, nothing else.
This is more like really toned-down 3E. In 3E you had the Psychic Warrior i.e. Psi-Knight, indeed I believe the subclass was previously called Psychic Warrior, wasn't it? And the Soulknife which is here called er, the Soulknife as the psionics + fighting and psionics + rogue-ing classes. You also had the Wilder (a bit like 3E's take on Sorcerer so yeah sorta vaguely kinda equivalent to the Psionic Soul sorcerer here), and the Psion. The trouble is the Psion has no equivalent here (the Psionic Wizard was a dismal failure as such), and also that the Psychic Warrior and the Soulknife were half-casters, so should be equivalent to the Eldritch Knight and Arcane Trickster, in that they should have access to the Psion's abilities, but only some of them. That should afford them a great deal of utility not evident here. Utility is something Psionics was strong at in all previous editions except 1E (but that was because 1E psionics were a random mess).
I personally played a Psychic Warrior quite a bit in 3E (my favourite 3E character), and the utility afforded by the psionic stuff was pretty huge, and a lot more interesting than the yawnsome combat stuff here. They could at least hand out a variant Mage Hand cantrip to both. Right now if you wanted to do a character like a Psychic Warrior in 5E, you'd probably want to play a Valor Bard, which is er, not how it should be.
The Soulknife subclass is at least charming (if ill-designed in some regards), and I have no particular issue with the Psionic Soul Sorcerer, but the Psi-Knight is pretty sad, because it has little of the charm of 3E and 4E psychic warrior types (I forget the name of the class in 4E), and fails to follow the recent trend of Fighter subclasses in actually having some non-combat utility.
If we translated 2E's Psionicist to 5E (and to some extent 3E and 4E's Psions), you'd probably end up with something most functionally similar to 5E's Bard, but with a quite distinct set of abilities. Hell, I'm going to say, had that previous article tried to "do a Psion" but used the Bard as the base instead of the Wizard, it might have got away with it, because it's a lot closer. There's a heavy utility and CC theme, and some healing with Psioncists and Psions. You want to do Psionics by way of magic? You start with the Bard or something close to it.
Interesting the "class feature variants" article makes this far more viable, because you could replace a lot of stuff. Even Inspiration works well as a Bard-Psion thing.