I'm curious if this method could be used along with super critical CO2 turbine generators. In other words after extracting the energy stored in compressed CO2, if you could then run it through a heat exchanger to bring it up to super critical temps and pressure and then utilize it as the working fluid in a turbine.

It looks from the diagram that a turbine is the energy extraction mechanism? As you'd expect.

Correct, going from cold compressed liquid co2 though. For supercritical CO2 one would then heat up the gas and use it as a working fluid to turn the turbines further.

If you could reuse the same turbine, one could store excess solar/wind energy in the compressed gas form, and then fire up a natural gas or biomass gasification reactor and then feed the heat into the system to produce more electricity on demand.