As others have pointed out, this is very different from saying that atmospheric CO2 levels have not increased. It does not claim that, in actuality far from it

As others have pointed out, this is very different from saying that atmospheric CO2 levels have not increased. It does not claim that, in actuality far from it. The gist of the article is about 65% of emitted CO2 is "sunk" into plant and other terrestrial sources. About 45% remains in the atmosphere. That's the "CO2 fraction," really a sort of ratio. That ratio has, apparently, remained about constant. However, despite the ratio remaining constant, the absolute value of atmospheric CO2 (in ppm) has still increased. It's interesting if you're putting together a climate model, where you have to make assumptions about the amount of carbon sunk versus remaining airborne, but I'm not sure of the significance to an average person.