Landauer's theorem relies heavy on the rules of equilibrium thermodynamics.  The assumption in equilibrium thermodynamics is that every action starts from an equilibrium state, ends at an equilibrium state, and that we don't care too much about what happens in the middle.  This experiment appears to rely on non-equilibrium thermodynamics, where we no longer assume that we start and end at equilibrium.

They explicitly mention this in the middle of the paper.  They focus on actions which can be done faster than the relaxation time of the system.  By doing this, they develop a structure which is physically reversible but logically irreversible.  They do mention that if the system is permitted to reach equilibrium, the circuit enters a state which "erases" the information.  If this happened, I do believe their MEMS element would be subject to the same energy costs that Landauer's principle predicts.  However, by making sure the logical measurements occur faster than that, they can stay within the realm of non-equilibrium thermodynamics and yield a *more reversible* logic element.

I believe this is sidestepping Landauer's principle simply by focusing on non-equilibrium states.  This is not an unreasonable approach.  It reminds me highly of the famous paper suggesting that bumblebees cannot fly, because a static analysis of their body and wingspan says that they don't have enough lift to fly.  Of course, everyone knew this had to be false, because we know bumblebees do indeed fly.  It took a while before we found out that they were using a dynamic approach to fly, creating vortexes with their wings which had the effect of amplifying the effectiveness of their wings.  The dynamic effects permit a bumblebee to fly using far less material than they would need to fly using simpler laws of flight.  Likewise, this experiment appears to use dynamic effects to use far less energy than would be needed using simpler laws of computation.