(Yes, I see that the article claims their system is a mere 10 to 30 times more energy efficient than conventional dehumidifiers. That still sounds far too good to be true.)
I recommend you look up how heat-pumps work: https://www.nrcan.gc.ca/energy-efficiency/energy-star-canada...
Energy is being put into the system but it is less than the AC unit cooling humid air on its own so is a net gain relatively speaking.
Why would it be a problem to do just the middle one instead of all three?
From the patent:
[The vacuum pump] is used to provide modest compression to raise the vapor pressure sufficiently to condense to liquid water. Because the compression work is only done on the water vapor, this minimizes the energy consumption. Lastly, the condensate is pumped up to atmospheric pressure for discharge to a storage vessel (this consumes a trivial amount of additional energy).
Update: The patent also implies that the high efficiency of any given device of this type may only obtain over a limited range of operating conditions:
Sorbents optimized for a 43.degree. C., 60% RH condition are likely to perform poorly and result in much higher power consumption at the more challenging 27.degree. C., 10% RH humidity condition and vice versa.