Can someone explain the maximum theoretical efficiency of this process from basic thermodynamic principles?
This is converting electricity into kinetic energy and vice versa. So it'd be the product of those two maximum efficiencies, whatever they are.
Where do you get that from? The article definitely seems to me to be describing a heat engine.
That said plenty of the steps involved here are likely not 100% efficient, and I'm somewhat unsure where they're recovering the energy involved in the gas-liquid phase-transition, if at all.