Isn't liquid oxygen cryogenic (boils at -183C)? The engineering of keeping that ...there... gets interesting fast, especially when dealing with all the cold (absorbed heat from expanding gas) and containing the pressure while also releasing oxygen slowly.
The oxygen gas is dissolved into a different liquid, some kind of perfluorate in this case. You can put more oxygen molecules in a given volume when dissolved in a liquid than if you just compress the gas.
But oxygen dissolved or otherwise absorbed in a material is fair game. Even without anything fancy, water can contain about 1% free oxygen, which is 8x what you could do with gaseous oxygen (which is in turn 5x what atmospheric mixture has).
And there are a lot of chemical reactions that can produce oxygen much better than 1%. The trick is going to be avoiding heat changes.
