A chimney would not suffice to keep the room comfortably cool.
That's a blanket statement, and hence a statement that is inherently incorrect.
In other words, it depends on the size of your chimney. One could easily remove 1MW with a natural draught chimney, but it would need to be very large. A fan would reduce the necessary diameter.
Does such a chimney/flue exist in the Doral premises? Who knows? There's certainly a big chimney cover on the roof. And do the published photos cover the entire volume of the "factory"?