Putting aside the appeals to emotion, this is what the law actually says:
Source and complete article:
Why are people talking about NY's abortion law?
In other words, the only two cases where a late-term abortion would be allowed would be where
1) The mother's life was endangered, and
2) The fetus wouldn't survive outside the womb anyway.
By the way, OP, your source is called "desiringgod.org." That is conspicuously biased, something that is compounded by the fact that the viability of fetuses and precisely when they are able to survive outside the womb are also topics that heavily tread into a medical and scientific territory—not a theological or dogmatic one.
For further reading, here's a Snopes article detailing the false rumors—mostly from conservatives—about the law compared to what it actually states:
FACT CHECK: Did New York Pass a Bill Legalizing Abortions Up to Birth?
Yes, putting aside emotions of a baby being terminated at 9 months or after birth...
It says: Furthermore, the legislature declares that it is the public policy of 15 New York State that every individual possesses a fundamental right of 16 privacy and equality with respect to their personal reproductive deci- 17 sions and should be able to safely effectuate those decisions, including 18 by seeking and obtaining abortion care, free from discrimination in the 19 provision of health care
Loop hole... if it is private, you never know why it was done...
It says "amended" :§ 6. Section 125.00 of the penal law is amended to read as follows: 6 § 125.00 Homicide defined. 7 Homicide means conduct which causes the death of a person [or an 8 unborn child with which a female has been pregnant for more than twen- 9 ty-four weeks] under circumstances constituting murder, manslaughter in 10 the first degree, manslaughter in the second degree, OR criminally 11 negligent homicide[, abortion in the first degree or self-abortion in 12 the first degree]. ...
...
DEFINITION. 17 The following [definitions are] DEFINITION IS applicable to this arti- 18 cle: 19 [1.] "Person," when referring to the victim of a homicide, means a 20 human being who has been born and is alive.
So... it is 9 months, in the womb and not matter what you do with it, it isn't a homicide. For that matter, if a husband decides he doesn't want to have the baby, and the mother does, and he kicks the womb until the baby dies (please look at the video... a baby), the most he can be charged with is assault.
Then, of course, we remember when we first placed the abortion law "when the mother is in danger" and look at it now.
It is easy to come to the conclusion that this is just the beginning especially if you can make the baby comfortable while alive and then decide to kill it. It is a pandora box.
Please tell this person, "You should have been aborted at 9 months"
He now is married and I believe is having children.