What about relative application numbers? These things are partially self-selected. The first thing that occurred to me when I read the main observations in the article* was, "What if the proportion of girls in the programs is higher because more girls (or parents of girls) want to participate in the programs?" Wanting to participate (and especially having parents who want one to participate) would not necessarily be correlated with intelligence anyway.
*- That 1) gifted and talented programs in New York are tending to have more female students, and 2) this cannot be explained by suggesting that there are more gifted and talented girls.
That's a very good question. I think the study of application to graduate departments at the University of California: Berkeley (often used in statistics textbooks as an example of Simpson's paradox) showed that what initially appeared as a bias in favor of male applicants was actually, when analyzed department by department, neutral admission or bias in favor of female applicants.
The self-selection involved in applying or not for a special program is surely relevant to analyzing bias, as you correctly point out. A different issue that other commenters here mention is whether participation in a school program at early elementary age has any necessary relation to adult career paths at later ages.
*- That 1) gifted and talented programs in New York are tending to have more female students, and 2) this cannot be explained by suggesting that there are more gifted and talented girls.