First, please note that while this answer is dated May 31, 2019, it may actually be much older and referring to a different tax year. The May 31, 2019 date is when this post was moved from the old AnswerXchange to the new Community, which had the unfortunate effect of erasing the original dates.
Second, if the gambling winnings are from the New York State Lottery and are more than $5,000, then they are taxable in New York State, according to Publication 140-W.
Please note that the law changed in New York for tax year 2019:
"Treatment of certain gambling winnings Beginning in tax year 2019, New York State withholding is required for any gambling winnings from a wagering transaction within New York State if the proceeds from the wager are subject to federal withholding. Also, the New York source income of a nonresident individual must now include gambling winnings in excess of $5,000 from wagering transactions within New York State."
Thus, for nonresidents, all gambling winnings over $5,000 and which are subject to federal withholding are also subject to New York State tax, starting for tax year 2019. See the Instructions for Form IT-203 Nonresident and Part-Year Resident Income Tax Return, page 3.
The tax bulletin you refer to needs to be updated.
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