Got any pics of the inner workings of this guy?
It would be nice to know exactly what's going on. My first guess, from the circa 1750s dating, would be a bypass valve much like the Austrian Butt Reservoir battery. On page 132 of Wolff writes, 'The brothers are identified as among those who developed the air gun. A butt-reservoir pistol is at hand, similar, in some o reservoir features, to the Austrian type. A ball-reservoir example, also a pistol, has been examined. Both are rather unique.'
There is also the 1862 Austrian Genie Korp specification about using CO2 in a pistol (for defending an emplacement with mines.) This predates any Giffards, so, it is possible that it was the Boulliet that was being referenced. As I've mentioned before, those big wheel cranked pumps seen in Vienna are not air pumps; they're CO2 pumps.