Text from link: "In isolation the process is only 25% efficient, but this is greatly increased (to around 50%) when used with a low-grade cold store, such as a large gravel bed, to capture the cold generated by evaporating the cryogen. The cold is re-used during the next refrigeration cycle.[8] Efficiency is further increased when used in conjunction with a power plant or other source of low-grade heat that would otherwise be lost to the atmosphere. Highview Power claims an AC to AC round-trip efficiency of 70%, by using an otherwise waste heat source at 115 °C."

I was being pessimistic about their claims. Theoretically you could likewise capture the heat from compressed storage, too. Plus, it didn't seem fair in the comparison to compressed storage to include efficiency gains from using residual heat from elsewhere during expansion as technically that heat is input energy.

This is suspect. It looks like optimism to me. I agree you can assist it, but with the intrinsic Carnot limitations added, I dount they can beat 25-30%. It still may be economic to save even 20% of energy that would otherwise be wasted,. That added waste at 115C can make the difference