This is really brilliant. They cycle between two chemical species that are thermodynamically very stable in our atmosphere, solid MnO2 and Mn2+. This is very smart as a starting point because you don't need to worry about the electrodes slowly rusting away (compare: related work with exotic/expensive/unstable rare earth oxides)

Also this redox couple charges at 1.6 V so oxygen production (which is bad in a cell that also evolves hydrogen) does not really happen (this takes 2.0 V or so)

Really exciting stuff.