Our definition of being "antigun" is extremely liberal. You support even one gun control measure and those heavily vested in gun culture refer to you as being "antigun." It's not that everyone in NYC is antigun, but rather some support gun ownship AND regulations, e.g., AWB, capacity limits, registration, mandatory training, red flag laws, permit schemes, background checks, no carrying outside of the home in busy areas, etc.
There is a compelling argument that that definition is the correct one. Rights actually tend to be nearly absolute in many senses or they cease to be rights and become privileges.
Suppose you support freedom of speech, but you want it regulated, bans on certain kinds, limits on how much people can post, registering your forum with the government, mandatory writing and speaking training, red flag laws to revoke your freedom of speech if you say things that might be harmful, permits to speak in public squares, background checks before you are allowed to post or give speeches, not being allowed to speak outside your home in crowded areas where it might bother people etc.
Now, that does sound awful stupid doesn't it?
This is usually where someone says something to the effect of "speech has limits too!", which while true, obviously does not turn the point.
The limitations on speech are similar to the legitimate ones on firearms. Ie. not shooting in a dangerous fashion, not allowing children to access them unsupervised, not shouting fire in a crowded theater, etc. Ie. where the action has an immediate result of endangering life and property. So shooting in the public square (in normal circumstances) is a no go, but carrying there is fine because it does not endanger anyone by doing so.
So it is quite reasonable to say that someone supporting those things does not actually consider bearing arms a right. Certainly if they wanted the same "regulations" on speech we would conclude that they don't support speech as a right. I would say someone who does not support the right (at least for those eligible) is anti-gun even if they support it as a privilege with stipulations (and in NYC those stipulations are basically wealth/power).