What process compresses a rooom full of 02 into that size?
Condensation. There's far less space between the molecules of liquids and solid than those of gases. The difference in density between water and water vapor is an example that everybody probably understands. One mole of water weighs a hair over 18 grams, and has a volume just over 18ml. The same mass as water vapor has a volume of 22.4 liters, or 22,414 ml. That means a given volume of water has 1245 times as many molecules as the same volume of water vapor (at standard temperature and pressure). In the case of oxygen, the liquid is 860 times as dense as the gas.
Of course plain old condensation wouldn't quite do the trick. A modest room that's 8.6 x 10 x 10 feet would have a volume of 860 CF, so condensed to a liquid the oxygen in the room would have a volume of about .209 CF (about half the actual physical volume of an AL 80). That much O2 would weigh about 14.4 pounds (860CF * .08 lb/CF * 20.9%). Let's assume the spoon the article referred to is a big ass cooking spoon with a volume of 4 ounces, and that the material itself is weightless. Bonding that 14.4 lbs of O2 to the piece of material with a volume of 4 ounces would result in a density of over 3000 lbs/CF, which is more than 4 times the density of lead. Compressing that O2 into a 4 ounce scuba tank would require a pressure of almost 43,000 atmospheres (at which point the ideal gas law won't apply, because the volume of all those molecules becomes significant).
This must be a very special material, indeed.
giving me visions of this:
Even if the material allowed you to absorb and immediately use the O2 dissolved in the water (and ignoring the problem of breathing 100% O2 at depths of more than 20') I still can't imagine that it would actually allow you to breathe. At 4 ATA and 0ºC the maximum solubility of O2 in seawater is about 45mg/L. A SAC rate of .5 CF/minute means you're breathing about 0.1 CF of O2 per minute, which is about 3.6 grams. At 99' you'd need 14.4 grams of O2, which means you'd have to use all of the O2 in 320 liters (320 kilos, 704 lbs) of water every minute. Solubility is proportional to pressure, so the same would be true at any reasonable depth, but solubility decreases as the temperature increases. Just moving enough water would require considerable effort no matter how efficient the absorbtion and exchange process is.
An ability to accurately blend bonded, low volume, O2 with N2 from a cylinder would potentially be useful. An AL 80 with 100% N2 would have the same effective size as a 117 CF tank of EAN 32. That would certainly allow for much longer dives or a greater margin of safety for those who don't pay enough attention to their SPG. On the downside, the need to blend O2 with a diluent would effectively make every OC diver a rebreather diver, with a chance to breath a mix that's hypoxic or toxic.
And of course there's still the matter of how to release the O2 to make it useful.