Okay. Looked it up and I’m not entirely right.
http://iopscience.iop.org/1748-9326/4/4/044011/fulltext/#erl323265s6.2
It is apparently possible to run such a hybrid with the fuel engine always operating at peak efficiency to either drive the vehicle or compress the air, then have it shut off when tanks are fully pressurized. A fuel engine operating always in its peak efficiency range is going to be much more efficient overall, so you are capturing energy efficiencies other than those associated with braking and slowing down.
I still suspect that by the time you run a complete analysis of energy used to travel 1000 miles it’s going to be tough to beat an efficient IC car by much, particularly the highly efficient diesels common in Europe but for unknown reasons not imported to here.
As anybody who has ever worked with compressed air knows, this process creates a LOT of waste heat. If they have found a way to use some of this heat it will help efficiencies considerably. The process also condenses a LOT of water out of the compressed air, which especially in humid climates will create some interesting challenges for the engineers.
That is an interesting study at the link you posted!
A little more here:
[The process also condenses a LOT of water out of the compressed air...]
[...running parallel to the exhaust.]
Perhaps placing the compressed air tank next to a heated source solves that problem.
But don’t forget that the weight of batteries is eliminated. That’s a lot of weight. But yeah, the 117 mph claim is hard to believe.