Ignore the semantic issue, and consider their actual argument.
Also it seems that b_b has considered their actual argument, and has responded to it in his/her post with his/her concerns.
As to your points about slavery, sacrifice, etc. I agree that what matters is how our current society views moral matters, not what generations past thought. Despite what moral absolutists say, history is clear that morals are relative. I think most people would agree that at this time in the West, killing babies is pretty universally abhorred. Plus, on the practical side, good luck getting any doctors (ya know, that whole "First do no harm" thing) to kill a healthy newborn. That would cause PTSD in even the most hard-hearted physicians, I believe. I don't know about Australia, where this paper came from, but pretty much every state in the US has laws whereby a mother can abandon a child at a hospital, or police or fire station, no questions asked. It seems to me that even if one can construct an academic argument in favor of infanticide, there is no practical room for it in a civilized society.
Given that morality is a system of accepted actions that benefit society (which I think is not too much of a leap), one can objectively say that things like slavery, murder, and rape are wrong.