They store the heat from compression and use it during expansion.

You can see it in the little animation on their website. It's marked TES (thermal energy storage).

It looks like their RTE is based on a 10 hour storage time. The RTE is going to drop after their sweet spot, but if they're just looking to store excess energy from solar farm for when the sun isn't shining that's probably not a huge problem.

Storing the heat is the key part, I suppose, even though they are focusing on storing CO2.

I wonder if something like the paraffin phase transition could be used to limit the temperature of the heat reservoir, and thus the losses during storage.