You are correct - that is truly a horrible lie. We now have seen federalism turned on its ear for Rudy - that it is "states rights" to ignore rights enumerated in the Bill of Rights.
That would only be valid if NYC seceded from the Union. Last I checked, it hadn't, so Rudy's (and this person's) logic is absurd.
The right of the PEOPLE is not the same as the rights of any individual person. Certain persons can be forbidden guns without it interfering with the right of the PEOPLE.
Hence, it is entirely constitutional to restrict gun ownership to the sane, non-criminals, those who can see etc.