It is being run by whatever creatures inhabit that other universe. Our actual descendants will live in this, the simulated universe.
And if they decide to run a simulation, they will simulate a less or different universe, meaning they will also not be simulating their ancestors (us).
The simulation argument relies on a loop of logic that is broken by entropy.
I see what you are saying, within the bounds of the article, the Basilisk, requires that our descendants are simulating our present. But by necessity, our genetic descendants would also be members of the simulated universe. Of course, they don't have to simulate the entire universe, they only have to simulate the local part that immediately affects what we do. So long as the model we're in produces equal results to "reality" it's good enough.
All simulation hypotheses discount two other kinds of descendants, intellectual "descendants" for one. Observers of the simulation who learn or are influenced by the simulants. Just like I might run a program on an emulated Commodore 64 and be exposed to some idea I hadn't considered before.
"Escapees" - e.g. Tron: Legacy, Agent Smith from the Matrix movies, The Doctor from Star Trek Voyager. Simulated mentalities which find an external host to "upload to". In the case of Tron movie, the particle laser thing constructed a body for Quora, in the Matrix movies, Smith uploaded his consciousness into a real human and in Voyager the doctor was given a portable hologram generator to let him leave the holodeck/sick bay. Any of these could potentially produce a long of descendants.
More importantly, our perception of time is unimportant from within the simulation. For example, if we assume the shortest possible unit of time is planck's time and call it a "frame", and it takes the computer running the simulation 10 million years of "external time" to simulate 1 frame. It won't matter to us, because we'll have only experienced 1 frame of simulation. Trillions of years could be passing in the real world while we're only ever aware of seconds passing.
So long as the hypothetical real computer can fit the simulation in some kind of memory, the simulation doesn't have to occur in 1:1 real time. It's like emulating a powerful computer on another more powerful computer. You might only get a few percent of the speed of the original, but from the point of view of the program running in the emulator, it doesn't know the difference.
If you have enough memory, you can even emulate a machine from the future on a less "capable" machine from the past. It'll be slow and horrible for you, as the person running the simulator. But suppose you're immortal? You pop in every few hundred years to see if Windows has finished booting.