That's true, but we're not talking about a normal situation here.>Asexual reproduction usually copies the whole genome
That's literally exactly what's happening here if you are assuming the only difference in the DNA is the X and Y chromosome. This would just be a straight copy of the whole genome. There is no normal way to run into a situation where the egg cell and sperm cell have identical DNA. Which is why this would be more akin to asexual reproduction.