Nope, it does not pull any carbon dioxide from air/water.
The oil with omega-3 acids is not produced from any algae, but from cultures of special strains of Schizochytrium.
Schizochytrium is a fungus-like organism (not related to true fungi). It is called "algae" in marketing language, because "Schizochytrium" or "Stramenopiles" are words unknown to the general population and because "algae" sounds more appealing to the rich vegans who have afforded to pay the high prices under which this oil has been sold for many years.
In any case, this does not matter much. Long-chain omega-3 are an essential fish food ingredient, but by mass they are a small fraction of fish food. Much more can be gained regarding carbon dioxide by using for the fish food a mixture of vegetable proteins that have been preprocessed to enable their digestion by fish.
Schyzochytrium has enabled the production of long-chain omega-3 acids without capturing small fish or krill for a few decades, but in the past the cost of Schyzochytrium oil was too high.
In order to be used as an ingredient in farmed fish food the cost of Schizochytrium oil had to be decreased a lot.
It appears that at least Veramaris has succeeded to do this, but unfortunately such progresses have not become visible yet in the retail price of Schizochytrium oil for human consumption.
A decade ago, Schizochytrium oil was 8 to 10 times more expensive than fish oil. Then its price has decreased, so that 4 or 5 years ago it already was only 3 times more expensive than fish oil.
Unfortunately, after that there were no further price reductions, so today the retail price of Schizochytrium oil is about the same as 5 years ago.
If the production cost of Schizochytrium oil has really diminished, as said in the parent article (because it cannot be used in fish food, unless it is cheaper than fish oil), then the producers have now increased profits, without decreasing the retail price. Of course, like always, it is not certain that this is really the winning strategy for them, because there may be many others like me, who wait for a reduction in the price of Schizochytrium oil in order to switch to it from fish oil, so keeping this inflated price may result in a much lower sales volume than with a smaller price.
Moreover, for whoever wants to consume vegan oil with long-chain omega-3 acids, there is an additional trap with Schizochytrium oil. The original Schizochytrium oil has a double concentration in comparison with fish oil (i.e. around 2 grams of omega-3 acids per 5 mL of oil), but there are many sellers who sell diluted oil at the same price like the sellers who sell non-diluted oil. Thus the true price of long-chain omega-3 acids from the sellers of diluted oil may be 10 to 20 times higher than from fish oil. Therefore when buying omega-3 capsules or bottled Schizochytrium oil one must read carefully the fine print and compute the price per gram of DHA+EPA, in order to be sure that the price is right.
To clarify for other readers... The point about "Schizochytrium is not algae" is that they do not photosynthesize and thus don't create sugars from CO2. Rather, this organism is a heterotroph and consumes various organic molecules from its environment. Industrial cultures are fed simple sugars and nitrogen sources, plus waste products like spent brewery yeast, cheese whey, and molasses.