Okay, having read the linked (translated?) article, I guess I'll chime in.
Regarding "dissolved air", the guy obviously knows the difference between air an oxygen, as the open vs. closed explanation made apparent, and I don't imagine anyone here questions that water can contain dissolved gases. That leaves the question of whether you can use a centrifuge to extract dissolved gases from water.
If you lower the pressure on a volume of water to a point where a portion of the dissolved gases come out of solution, you can certainly get bubbles. (Hehe, can we call it "bent water"?) If you bring that volume of gas and water back to its original pressure, the equilibrium state will be for the gases to return to solution. Your two options, then, would be to remove the evolved gases at the lower pressure (suck the bubbles and use a pump to increase the pressure to ambient), or allow the fluid to return to ambient pressure and extract the remaining bubbles before the gases return to solution. I would venture to guess that the former is the method the device in question would use, as I do not believe the transient mixed phase flow would survive long enough for useful extraction, but I could be wrong.
I find no inherent problem with the concept of extracting some of the dissolved gases from the water, although I am skeptical about the described energy requirements. I am far more curious, however, when it comes to asking what gases are dissolved in seawater at a given place and time as well as how significant water quality (dissolved gas profile?) would be to a theoretical "mechanical gill".
My knowledge of rebreathers is not adequate to formulate useful questions as to the composition of the evolved gases, but I would imagine the possible gases involved as well as the water vapor component (it would certainly be humidified) would be important considerations.
(Incidentally, this would seem almost completely useless below the thermocline in the lakes near me. I've seen their oxygen concentration and temperature vs. depth graphs, and there's almost nothing to breathe down there, even if you had a great mechanical gill.)