That's not what the paper described at all. Even the article explicitly said that the birds could only mate with 25% of the population -- the "opposite sex" alo

That's not what the paper described at all. Even the article explicitly said that the birds could only mate with 25% of the population -- the "opposite sex" along two dimensions, instead of just one. Those "special mutations" on chromosome 2 result in a chromosome that cannot recombine like a normal chromosome -- a new separate sex chromosome.