"That would be relevant if the chess winning programs mimicked the way humans think -- so that the same intelligence could be transfered in other fields."
That implies that, in humans, intelligence in chess can be transferred to other fields. I pointed out that that certainly isn't universally true. I think that correlation is fairly poor.
I also think the correlation between IQ and great chess playing is not that great, but don't have evidence for it. Chess playing _ability_, maybe, but good chess playing requires lots and lots of rote learning that the brightest humans might find too dull to spend their time on.
Also, one can argue that your claim that humans "prune much more intuitively and effectively than AI chess engines." isn't true anymore. Humans prune more, yes, but they also cannot beat today's best computers, so the 'effectively' part is up for discussion. Maybe, they are pruning too much? Or is it just that their evaluation function is inferior?
Well, for one, great chess players are generally of higher IQ. So great chess and increased general intelligence ARE correlated.
Now, why should being good at chess also apply to "protein folding"? If anything, following my logic it would be the opposite: protein folding is more like number crunching than like the way human chess players think about moves. If humans played chess like computers, then yes, they would also be good at protein folding. But humans do differently. For one, the don't actually consider millions of possible future moves. They prune much more intuitively and effectively than AI chess engines.