From what I read, there are numerous states whos citizens are allowed to buy here in NY (like per the Walmart sign), but NYS Penal law says it must be a contiguous state for a NY citizen to be able to buy there and transport here.
S 265.40 Purchase of rifles and/or shotguns in contiguous states.
Definitions. As used in this act:
1. "Contiguous state" shall mean any state having any portion of its
border in common with a portion of the border of the state of New York;
2. All other terms herein shall be given the meaning prescribed in
Public Law 90-618 known as the "Gun Control Act of l968" (18 U.S.C.
921).
It shall be lawful for a person or persons residing in this state, to
purchase or otherwise obtain a rifle and/or shotgun in a contiguous
state, and to receive or transport such rifle and/or shotgun into this
state; provided, however, such person is otherwise eligible to possess a
rifle and/or shotgun under the laws of this state.