The firearm transport rules you allude to would not apply to this case.
Lawful federal transport of a firearm requires that you have lawful possession of it at both the starting and ending points of the transport.
In this case, within New York, the individual did not have lawful possession of the handguns, and was in probable violation of New York City, New York State and Federal law as a result.
I think that these draconian anti-gun owner laws are unconstitutional, and also inappropriate, but as we stand, they are on the books and enforceable. A Supreme Court challenge could take years to weave it's way through the layers of courts involved. In the meantime, one of the impacts of being convicted of a felony violation of firearms law is that you become a prohibited person as well.
The very fact that legislatures have passed these laws is certainly problematic, but I would never volunteer to be the test case for one of these legal actions. The fact is that if a legislature passes such a law, and no court chooses to finally reverse it, the law stands. That is how our system works.
I have studied Second Amendment law, and the origins of the right to bear arms. I also contribute to introducing legislation in my own state to correct such abuses as a director of our state's gun rights organization,
GRNC.
Please see some of
my Blog for more on this, rather than discuss the politics of this here.