I have to say I find this very unlikely due to several reasons, first of all it doesn't really explain anything.
The first problem you run into, which will eventually as far as I see it, bring everything down is who or how did the first simulation get started?
Next the issue is regarding computer power which seems to be based on a wrong assumption. Which have to do with there only being one reality, that is those who created the first simulation. Therefore computer power doesn't work as it is outlined in the paper, but is most likely an exponential factor of unimaginable proportions. The reason for this is that the computer power needed will have to be calculated solely based on the original creators capacity of running all simulations they created, including all the simulations that those simulations created until potential infinity.
So if the original creators created 50 simulations, which each also create 50 simulations each, would require the original creators to having to run 2500 simulations at the same time, as these are the only ones with actually energy and computer power that is not an illusion/simulation.
The paper assumes that we would be running ancestor simulations and therefore its also likely to assume that these simulations look like the Universe we live in or at least with the same complexity. So having to calculate the total amount of computer processing power needed for simply running 2500 simulation, where infinity is "maximum", would be considered fairly few simulations, but the power required astronomical even for that.
If each of these simulations are controlled individual by the "simulation" that created them and being unaware of where in the chain of simulation we are, it would also mean that the chance of our simulation being terminated would be extremely high, unless we are at the top of chain.
Furthermore you have to look at the complexity of the simulation it self, even though we can not observe everything in details at a given point in time, all the variables that controls our Universe would need to be updated or calculated down to every single detail or we would find errors in it. So the argument that it is not necessary to keep track of unobserved things or matters, would only reduce the amount of computer power needed slightly. But when so much is already needed it would be surprising why the simulation would not run this constantly.
So to me at least, it seems fairly unreasonable for this to be correct and also makes no attempt to explain how the first humans created their first simulation. Last what on Earth is "posthuman stage"?