Some of the claims in the article appear highly unlikely. I think they overestimate population in the Americas pre 1492 by at least a factor of two.
For a discussion of pre-Columbian population levels and the epidemiological effects of the Columbian Exchange, see
Secret Judgements of God, I don't have the author. Not a long read, but a pretty thorough documentation of the effects of European and African diseases on the New World populations.
The title refers to what one Spanish imperial writer thought about the great reduction in New World population, and his attempt to account for them. De Soto found the Indian villages of Florida already decimated by disease; the epidemics had struck a generation before his arrival; and New Englanders frequently found abandoned Indian villages, too.