In a game this is likely done as simply a prerendered animated texture (atlas).
Perhaps in a modern AAA game you might try a GPU particle system with 10k+ particles.
I suspect it depends more on what the developer knows. You certainly don't need to be AAA to do particle smoke, I've done webgames with particle smoke in JavaScript.
With the right tech artist, this sort of shader is essentially what their job is. ShaderToy shows how much you can do with a quad and enthusiasm.
Back in the days of the PS2, you’d just take a couple of long triangle strips, give them a twist or two, then UV-animate a static texture up through them.
Particle systems can be very efficient. Modern ones are designed to be able to build this kind of shader from a GUI. If you don't use any kind of physical simulation (and this doesn't), you wouldn't pay for it.
You could build this same set up in a particle system and then have convenient knobs (like physics) to turn on for higher quality instances.
