As a complete amateur, my understanding is that some of the oldest Mayan towns and cities rose in Guatemala and then the Mayan civilization spread into the Yucatan. Places like Tikal and Copan were long past their heyday when cities like Chichen Itza rose to importance. And like you said, the Classic period ended a few centuries before the Spanish showed up. But the article is mistaken to suggest one drought ended the Mayan civilization.
I think that is a good point. Tikal was abandoned by 950 AD but Chichen Itza lasted until the 13th century.