[thespoonbends]

It does not.

It mentions "One might posit that people with lower cognitive ability have higher risk of catching the virus. We consider such a relationship plausible; however, it would not explain why the observed deficits varied in scale with respiratory symptom severity.".

That is, it attributes that potential causal link as raising incidence of infection (e.g. they may choose to gather in crowds indoors), not as raising the impact of infection.

Either way, as a cross-sectional study, it doesn't establish causation, but may be a smoking gun.