On the assumption that IQ and "chess skills" both contribute to "chess performance", then everyone achieving a threshold of "chess performance", such as being an "elite player", has been selected to have at least a certain sum of "IQ + chess skills".
This means that, given high IQ, it's not necessary to have good chess skills to be in the elite group, whereas given low IQ, it is necessary to have good chess skills to be in the elite group. This will establish a negative correlation between "chess skills" and IQ within the elite group even though they are positively correlated overall.
Similarly, SAT math and verbal scores tend to be negatively correlated within the student population of any particular university, because universities will reject applicants whose total scores are low, despite the fact that the math and verbal scores are very strongly positively correlated in the larger population.
This means that, given high IQ, it's not necessary to have good chess skills to be in the elite group, whereas given low IQ, it is necessary to have good chess skills to be in the elite group. This will establish a negative correlation between "chess skills" and IQ within the elite group even though they are positively correlated overall.
Similarly, SAT math and verbal scores tend to be negatively correlated within the student population of any particular university, because universities will reject applicants whose total scores are low, despite the fact that the math and verbal scores are very strongly positively correlated in the larger population.