That is roughly accurate for describing the operation of real compressors.
The reason for calculating the bare minimum "magic compressor" cost is because it also applies to techniques like pressure-swing adsorption:
https://en.wikipedia.org/wiki/Pressure_swing_adsorption
Using PSA can reduce the energy cost of CO2 extraction significantly relative to direct compression technology. But because we know that the adsorbent is used in a cyclic process, we have dW[compression] = p dV + dE[adsorbent] and the long-time integral of dE[adsorbent] is effectively zero because the adsorbent cannot absorb or release energy forever, so ΔW[compression] = int[p dV] and thus any technology, compression-based or not, incorporating some finite amount of external components, is subject to the work limit.
This is also why, for example, thermodynamic analyses of engine types are always concerned about the possible compression ratio. You could consider the partial pressure of atmospheric and stored CO2 as the compression ratio of a hypothetical compressed-air motor, which can then be run to extract thermal energy (i.e. violate the second law of thermodynamics) from any process more efficient than 500 J/kg CO2, since again W[motor] = int[p dV]. You can improve the compression ratio by taking advantage of the P-T curve and performing the whole compression at the South Pole, which saves you about 100 J/kg.
Also, I was off by a factor of ten when I plugged in the vapor pressure of CO2. Correcting this is left as an exercise to the reader.
Technologies not subject to the work limit include e.g. olivine crushing, somehow inhibiting volcanic activity (???), planting trees, etc. Another technology I just thought of would be to to form CO2@H2O clathrates in seawater starting with air, which would also lower the compression ratio, and extracting the (solid) clathrates to recover CO2 and desalinated water. Here the pressure required is much lower and additionally desalinated water is produced; this only works if we form the clathrates in a cold environment and decompose them in a warm one, which is kind of inconvenient. Then again, shipping gigatons of fresh water to LA might become necessary anyway!