Based purely on numbers CO2 capture seems like a plausible idea. The article cites a cost of $0.22 cents per liter of fuel to capture an equivalent amount of CO2. Based on the current 93 million bbl or roughly 15 billion liters of oil consumed every day worldwide, the cost would be around 1.2 Trillion USD per year, or 1.5% of the global GDP. A lot but within the real of feasibility.
However to achieve that in practice we would need to build enough CO2 capture plants to capture the CO2 released by all human activity, and we've been building machines that release CO2 for decades. The effort to catch up is immense. The similar company Climeworks, cited in the article, has an example of such a plant here : http://www.climeworks.com/our-products/. The DAC-18 variant, which looks like the prototype that they actually built, it is a complex 3 stories high structure with 90m^2 of ground area, and according to the product page it can capture 2460 kg per day, although that is probably under ideal conditions and in practice it could be considerably less. According to a quick search we released around 36.75 Gt of CO2 last year. To capture that, we would need to build 36.75e12/365/2460 = 41 million such plants, at the bare minimum. And that would be only break even, we'd need even more to start capturing the excess CO2 already in the atmosphere. That seems unrealistic.
However to achieve that in practice we would need to build enough CO2 capture plants to capture the CO2 released by all human activity, and we've been building machines that release CO2 for decades. The effort to catch up is immense. The similar company Climeworks, cited in the article, has an example of such a plant here : http://www.climeworks.com/our-products/. The DAC-18 variant, which looks like the prototype that they actually built, it is a complex 3 stories high structure with 90m^2 of ground area, and according to the product page it can capture 2460 kg per day, although that is probably under ideal conditions and in practice it could be considerably less. According to a quick search we released around 36.75 Gt of CO2 last year. To capture that, we would need to build 36.75e12/365/2460 = 41 million such plants, at the bare minimum. And that would be only break even, we'd need even more to start capturing the excess CO2 already in the atmosphere. That seems unrealistic.