Are human males and females more genetically different than members of other species?
I'm not sure I buy your premise: firstly, the degree and form of male-female differentiation in social roles has varied widely across time and culture in human history so I doubt it forms a uniform evolutionary driver such as you describe. Secondly, the degree of male-female differentiation appears to me to be much greater in species such as gorillas, lions and peacocks than it does in humans so I'm not convinced that humans would stand out on this front as a species we'd expect to have greater genetic differences.

Even so, the only genetic difference between male and female humans is the Y-chromosome. The X appears in both males and females and doesn't have exclusively female lineage so it can't acquire separate genes for male and female. The Y chromosome contains very few genes so its not capable of manifesting a major genetic gap and because there is no recombination in the Y chromosome it is not a fertile ground for new genes anyway.

So males and females have essentially the same genes. However, this isn't the whole story because how, when and whether genes are expressed is about as important as what genes are encoded anyway. It is these differences that enable big differences between the sexes not actual coding differences.