Someone should dig into who this is coming from and why. The answers are usually either (a) they got paid to do it by a company selling the tech, which appears not to be the case here, or (b) they went insane on social media.
(can't confirm this personally, but it seems from other comments that it's perfectly feasible to just drive out of New York State and buy a gun somewhere else in the gun-owning US? And this is quite likely where all the guns used in existing NY crime come from?)
I would also note that the Shinzo Abe doohickey wasn't 3D-printed.
Printing barrels and FCUs -- the fire control unit, which is the only thing tracked and serialized in a gun at least in the US -- is more difficult but not impossible. Actually, building a functional FCU that can strike a bullet primer, or a barrel that can be used once is not difficult at all and if you look around you can find videos of people that have tested that with a mixture of 3d printing and rudimentary metal working skills. The major issues on designing those parts are reliability and safety. In the Philippines there is a full bootleg gunsmith industry dedicated to build illegal guns that match commercial ones in those aspects too.
Sadly, instead of having better laws we get fallacy rhetoric by people who probably have never touched, much less fired a gun in their lives.
If you look at how Apple detects contraband imagery, they hash every image that gets uploaded into the photos app. Those hashes are transmitted to servers that compare them to hashes of known contraband.
A similar system could theoretically be used for STL files. So it isn't about detecting exact shapes, it's about preventing printing of STL files that are already known to be dangerous. This would make it harder to illegally manufacture parts for weapons because it would make it much harder to share designs. If you didn't have the knowledge or skill to design a reliable FCU, you would have to find a design someone with that knowledge and skill created - which the printer could theoretically detect with a cryptographic signature.
As the original author of the post pointed out though, this could and would be bypassed by actual criminals. As with most things like this, it's probably impossible to prevent entirely, only to make it more difficult.