While the blog post you linked to claims that the work finds "implausibly large effects", it doesn't clarify what the author finds implausible about them (and the author admits to only spending 30 minutes looking at the literature).
I would agree that the graphic in the PDF linked in this HN discussion, and in the paper referenced by the blog post you cited, uses alarmist labels (e.g., "dysfunctional" for performance scores at 25th percentile and below). However, the full version of the report, as linked by post, states that the percentiles are based on the reported scores from 20k other administrations of the test.
Therefore this report simply implies that some of the reported variation in some of the historical scores might be explained by variations in room CO2 concentrations. What's so implausible/impossible about that?
Disclaimer: I know several of the authors of this report, and have good regard for their scientific integrity, so my gut-level reaction to an undocumented accusation that their results are implausible, was skeptical.