But actually that article is pretty thin. I believe it was originally a joke about how many astronauts are from Ohio, so they'd get to space and it would turn out the whole planet was Ohio. It is in fact a reference to real world thing, it's just a very obscure and absurd reference.
Internal combustion engine based generators aren't fancy steam engines either - however, they have a lot in common still. It's still just a way to move around the spinny bits of an alternator/generator/dynamo/whatever
There's one more outlier though which is Electrochemical cell, like galvanic element or voltaic pile
It was used around 1800 as a major electricity source, but I guess it quickly became uneconomical in 1866 or sth when the dynamo was invented.
Edit: wait yes, it actually says this in the second paragraph of the linked article:
The entire 19th-century electrical industry was powered by batteries related to Volta's (e.g. the Daniell cell and Grove cell) until the advent of the dynamo (the electrical generator) in the 1870s.
So my general understanding is that you can use a magnet to create an electrical current. Its like it pushes the electrons, like a paddle pushing water. So they coil a bunch of wire around a magnet and rotate the magnet, which moves the electrons in the wire and that gets you electrical power. But you need something to push that magnet around, so you attach that to a big ass fan and use steam to push the fan. That's your turbine. Nuclear power is just using a hot rock to make the steam. Hydroelectric power uses a river to push the turbine. Wind power is doing the same thing, just uhhh, with wind.
Turning heat into mechanical or chemical or electric energy directly is really hard, you know.
It's funny that you can get more energy from gas by using it to heat water and using a steam turbine to drive whatever. It's just not always practical.
I'm not really sure how else you'd do it. The energy we can get out of fission is in the form of heat, and steam isn't as compressible as just gas and it's easy to make with just heat. Combine that with electromagnetism giving you electricity by spinning some magnets around some coils, and there you go.
It's probably possible to get some air hot enough and do some fancy convection work to get it to spin a rotor, but that's going to be really inefficient.
You could also use the heat to make materials glow and put a solar panel nearby, but that's also going to be pretty inefficient.
It's just taking advantage of the change in matter state. H2O expands ~16,000 times it's size when it boils from liquid water to gaseous steam. That increase in size means it wants to go somewhere else, we just control where it goes and it's relief valve happens to be going through a spinning wheel with magnets on it, inducing currents in the coils of wire around the wheel.
Yes it's way more complicated than that, but it's the best way we have of turning heat into electricity, so it's what we use. With the primary exception of solar, nearly every form of power production is using heat energy to indirectly spin a wheel.