Yeah, the argument assumes that the simulation is the "detail-on-demand" kind, meaning that when the simulated people run their own simulation, the real computer in base reality has to provide a tremendous amount of new detail -- roughly the same amount as is allocated for their world (assuming they run the same kind of simulation as the one they occupy).

So, for example, if the sims have just 10 simulations running simultaneously, the simulation they occupy will consume 11 times more computational resources than before (including memory). Even if the computer in base reality grows to the size of an entire galaxy, just one more level down means now you need ten galaxies. All this just to keep your single sub-simulation-incorporating simulation running.

I think it's more likely that the simulators will nip the problem in the bud by halting the sim just before sub-simulations become possible, thus also preventing sub-sub-simulations and sub-sub-sub simulations and so on. After all, the thing they're probably simulating is their own historical singularity, so once sub-simulations become possible, the simulation has pretty much run its course.