It seems weirder to me than that. Let us take it as a given that there really is a stereotype threat and/or that women are systematically discriminated against with regard to acquiring math skills. Let us take it as a given that damage is really being done. The natural conclusion is that regardless of what name is put on the top of the test, the women should
still do worse, because they really are worse at math at the time the test is being given, which is to say, after 15-20 years of systematic discrimination. If the discrimination is effective, then by definition it must mean they really
are worse. If they aren't worse, then the discrimination is either ineffective, or women are naturally
better at math and the discrimination is holding them back (a position which would be quite complicated to establish and defend).
If the damage can be undone by merely putting a different name on the top of the test, then that strongly implies that the putative damage is itself illusory. If the damage can be wiped away so easily, then it can't have been that bad in the first place. If this is the extent of the "stereotype threat", then it's obviously not holding them back all that much if even so their real skill is equal to the men's.
I can't help but think that this study was indeed ideologically driven, and in the zeal the authors had to prove their point about how women aren't worse than men, they didn't think about the fact this accidentally "proves" that the discrimination can't be that significant. But perhaps it is just a neutral study performed out of sheer curiosity.
And just to make it perfectly clear, I am taking their own logic on their own merits. I'm not inserting my own opinions here, excepting on the question of whether there was potentially an ideological drive here. (My opinion doesn't really fit on this axis at all either way.)