As far as I know, zinc pyrithione isn't available in any consumer product, because it is pretty toxic in moderate levels. Without it (from the article) "the concentration of free Zn2+ is maintained at a relatively low level by metallothioneins".

Zinc supplementation may of course help if you are deficient, but the study can't really tell if 'healthy' Zn2+ concentrations contribute anything to the inhibition of viral replication.