The rule made sense at the time as propeller engines are far more likely to fail. Overtime it became apparent that modern jet engines are extremely reliable and the need for the third engine wasn’t necessary.
It's mentioned in the article, and it didn't just kill off 3-engine planes, but 4-engine planes like the 747 as well. The Airbus A350 XWB has a ETOPS-370 rating, meaning it can fly up to 370 minutes (over 6 hours) on a single engine, or between any two points across 99.7% of the world.
It can fly almost indefinitely† on one engine. Performance is reduced, but it can even still climb. That ETOPS rating means this plane is allowed to fly routes planned at up to 370 minutes over water with two engines in the expectation that when sooner or later it experiences an engine failure the one remaining engine can get them to safety so often that regulators are willing to accept the residual risk.
If you call up the regulators and say "OK, I have an A350 here, but one of the engines doesn't work, can I fly that over an ocean to get it fixed?" they're not going to issue you a ferry exemption justified by ETOPS, they're going to say "No". ETOPS is about what you can do with two engines knowing what will happen if one fails.
† Obviously it will eventually run out of fuel. And engines can fail, although that's rare, the core idea of ETOPS is that so long as these failures are rare enough we don't need three engines.
If you lose both engines mid-way across the Atlantic, I assure you that your twin engine ETOPS qualified airliner is not going to reach to an airport. The Azores Glider made it over 100km after losing its second engine which sounds very impressive -- until you look at a map of typical ETOPS authorised routes. If they'd continued on their original course when they at first didn't understand what the problem was, instead of diverting, they'd have been forced to ditch in the ocean.
Now, ditching an airliner in the ocean isn't certain death. But it's very dangerous and there is no margin for error. While the Hudson River is not exactly a welcoming experience, being very cold and more than deep enough to drown, it's much more favourable than an ocean.
So, ETOPS is focused on the very low but non-zero probability of losing another engine and so likely loss of life from what may then become a forced ditching of the aircraft.
Oh well, I thought it was going to be entertaining and factually accurate enough. Now I am questioning my memory.