I don't know if we live in the simplest universe giving rise to life for some philosophically and deeply "correct" notion of simplicity. However, I don't think this is needed for the argument in my post you are asking about. In fact while writing that post I was implicitly assuming that the attacker's universe is about as complex as our own, in order to make my argument harder.

First, I think that if we write down a particular universal prior (e.g. by choosing a universal turing machine like a Python interpreter), then we probably won't be the simplest:

• The actual simplest universes will be different across different programming languages. This is plausible because those universes are themselves simpler than implementations of universal Turing machines without preprocessing. But it's very hard to really know.
• If you believe this, then it's unlikely that we have the simplest universe according to say the Python prior, or any other concrete prior we write down. There's just one "right" prior according to which we are the simplest.
• Even if that prior were philosophically distinguished, that doesn't help us unless we do that philosophy and pick out the right universal prior.

Even if we did live in the simplest universe according to the chosen universal prior, it seems like we'd probably get a simulation:

• The anthropic update (including the inference from the language choice) is a huge advantage for simulators.
• It doesn't change the story that much if we get a simulation from a universe with our physical laws vs other physical laws.
• The awkwardness of reading out bits, and ensuring that evolved life has maximal control over that channel, probably puts you somewhere other than the absolute simplest universe.

Aside from the arguments I had in mind while writing the post, there is a more philosophical reason (that I've thought less about) to think that most early civilizations we care about aren't living in the simplest universe:

• I expect that "most" early civilizations are in "dense" universes, at least if you try to weight them by their intrinsic moral worth.
• I expect that it's simpler to create truly humungous simple universes with a lower density of life. Note that the complexity differences we are talking about here are very very small.
• Some of those universes will still allow consequentialists to control arbitrary output locations, despite starting from a very low density (e.g. faster than light travel would be very helpful).

That said, I do think that a lot of future influence comes from huge simple universes with easy travel, even if most early civilizations (by moral weight) aren't in such universes. And if you care about the moral weight of our civilization itself then I think it is plausibly dominated by the simulations, such that weighting by "future influence" is the only real weighting that's meaningful to apply to early civilizations.

For an answer that follows a very different intuition, take a look at Does Cosmological Evolution Select for Technology? by Jeffery Shainline. This is up there with aestivation and infinite ethics on the fun idea scale. He gives a nice summary at 2:13:23 on Lex Fridman's podcast to around 2:38. Highly recommend listening to the relevant clip on Fridman, it's pretty great. The entire episode is really interesting, and also contains some other supporting context for Shainline's arguement. Caveat: I haven't read the paper yet. The abstract is:

If the parameters defining the physics of our universe departed from their present values, the observed rich structure and complexity would not be supported. This article considers whether similar fine-tuning of parameters applies to technology. The anthropic principle is one means of explaining the observed values of the parameters. This principle constrains physical theories to allow for our existence, yet the principle does not apply to the existence of technology. Cosmological natural selection has been proposed as an alternative to anthropic reasoning. Within this framework, fine-tuning results from selection of universes capable of prolific reproduction. It was originally proposed that reproduction occurs through singularities resulting from supernovae, and subsequently argued that life may facilitate the production of the singularities that become offspring universes. Here I argue technology is necessary for production of singularities by living beings, and ask whether the physics of our universe has been selected to simultaneously enable stars, intelligent life, and technology capable of creating progeny. Specific technologies appear implausibly equipped to perform tasks necessary for production of singularities, potentially indicating fine-tuning through cosmological natural selection. These technologies include silicon electronics, superconductors, and the cryogenic infrastructure enabled by the thermodynamic properties of liquid helium. Numerical studies are proposed to determine regions of physical parameter space in which the constraints of stars, life, and technology are simultaneously satisfied. If this overlapping parameter range is small, we should be surprised that physics allows technology to exist alongside us. The tests do not call for new astrophysical or cosmological observations. Only computer simulations of well-understood condensed matter systems are required.

I guess I've always had a vague intuition along the lines that, if you built a game of life of ~ the scale of our universe and started it in a random initial configuration, that there would be many rulesets that are:

1. Simpler than our laws of physics.
2. Have a high probability of producing self-preserving and self-replicating patterns after enough time.

Then, I'd expect intelligence to arise convergently as a useful strategy for the patterns to perpetuate / replicate themselves in the game of life's selection environment.

This is also known as Simplicity Assumption: "If we randomly select the simulation of a civilization in the space of all possible simulations of that civilization that have ever been run, the likelihood of picking a given simulation is inversely correlated to the computational complexity of the simulation."

In a nutshell, the amount  of computation needed to perform simulations matters (if resources are somewhat finite in base reality, which is fair to imagine), and over the long  term simple simulations will dominate the space of sims.

See here for more info.

Questions like this highlight how misguided the current state of anthropic reasoning is. 

When one spends enough time thinking about the anthropic principle it would seem quite reasonable to raise this question. But take a step back, and consider it a physical/scientific statement: "The universe is likely in the simplest form that could support intelligent life". It is oddly specific. Why not say "the universe is likely the simplest that could support black holes?", or hydrogen atoms, or Very large-scale integrations? Each hypothesis results in vastly different predictions of what the universe is like. Why favor "intelligent life" above anything else?

People may provide different justifications for this preferential treatment. But it always boils down to this: We are intelligent lives. And it is intuitively obvious that the physical existence of oneself is important for their reasoning about the universe. But the Copernican science paradigm has no place for the first-person perspective. It requires one to "Zoom-Out" and think from an impartial outsider's view. This conflict leads to awkward attempts to mix the outsider's impartiality and the first-person self-focus. It gives rise to teleological conclusions like the fine-tuned universe which is often used as proof of God's existence. And less jarringly but far more deceivingly, regarding oneself as equivalent to the result of imaginary random sampling. It is perhaps unsurprising that anthropic problems often end up as paradoxes. 

To resolve the paradoxes we have to at least be aware of which viewpoint we are taking in reasoning and make a conscious effort not to mix first-person perspective with the impartial outsider's view. To lay all the debate to rest we perhaps need to develop a framework incorporating the first-person perspective into the scientific paradigm.