If you compare the female and male world records for pretty much any sport, you'll very clearly see the effect of SRY and other male-making genes.

The rationale for the female category is to remove this male advantage from competition. Allowing a subset of males who have the advantage of their sex to compete against female athletes, just because these males call themselves women, undermines the whole point of women's sport.

This is why we need such testing as described in the article. It's no different in principle to, for example, weigh-ins in boxing that enable fair competition in each weight category.