I've been there twice. Most recently two years ago. I was under the impression that they were unsure of why the society declined and disappeared. I was more under the impression that it may have been do to climatic factors.
I think the writer had a bit of a problem crafting this sentence. Plus, here and there, he shows some bias against European and American settlers. So, while there were indigenous peoples in later centuries who did die because of new diseases brought in by settlers, there's no evidence that this was true of Cahokia. You're right, it could have been climate-related, but every possible cause is speculation at this point, and the final decline of Cahokia remains a mystery.
In the history books I've seen that are more than about 5 years old, they always talk about a mysterious, unexplained decline in Indian population after 1500 or so.
In the things I've read that were written less than about 5 years ago (like this book), they invariably talk about a huge population decline caused by foreign diseases, to which the Indians had no resistance.
So I guess history writers feel the mystery has been solved.