Note that it's a New York state regulation, not New York City; upstate New York is not very dense.

On emissions, I couldn't find a good source on exact requirements, but 1990 onwards (generally nobody is importing a Kei car that's from before 1990, as that'd be 11 years beyond what's necessary for legal importing) had supposedly-strict emissions standards according to a few different sources.

A fun note on safety is that if you were to only care about driver safety as a rationale...then bikes of all kinds should be illegal. The situation in US law on safety regulations is frankly absurd, in that anything on 2/3 wheels gets a pass for safety if it has the most basic of lights, despite motorcycles and 3-wheel ATVs being by far the least safe forms of transportation, while a 4-wheel ATV that is at least double as safe is generally illegal (my state and a few others being exceptions), and then Kei cars that are like triple as safe are also illegal in many states, and then a regular-sized car is legal.
It is patently absurd that safety regulations that only care about occupant safety are used as a rationale to ban vehicles that wouldn't be banned if they were LESS safe for occupants. But ultimately, what it's all really about is that <4 wheels weren't mainstream (before ebikes, the only time anything came close to challenging cars was mopeds, and those weren't outselling gas cars, but ebikes are outselling ecars!), and the extensive safety testing of cars in the US that disregards international standards entirely, requiring fresh US-testing is a form of regulatory capture to make 4-wheeled foreign competition all but illegal. The 25-year rule was in part because cars that old weren't serious competition, but now that the tech has stagnated for ~25 years, they suddenly are, and so of course all of a sudden you get states interested in banning the most widely-known cheap small car imports.