I'm guessing the diagram is missing a bit on the heat exchanger side; they're going to need to dump plenty of (environmental) heat into the expansion thingy to keep the liquid CO2 boiling off indefinitely at the pressure they want.

If this is intended for small-scale to medium-scale on-premise storage then the evaporating CO2 could also serve as the cold side of a building-size AC system for extra efficiency during the high demand portion of the duck curve.

I think there may be quite a market for maintaining hot and cold (and pressurized/liquified) sinks throughout the day/night cycle in highrises or entire cities.