Yes, that amount is taxable in New Jersey.
"Nonresidents’ gambling winnings from New Jersey sources are subject to the New Jersey Gross Income Tax in the same manner as the winnings of residents. N.J.S.A. 54A:5-8(a) 5. This means that income received by nonresidents from lottery or wagering transactions in New Jersey is income earned, received or acquired from sources within this state, and is subject to New Jersey Gross Income Tax. For example, winnings from casino betting and wagering, New Jersey Lottery winnings on prize amounts exceeding $10,000, winnings from slot machines, raffles, bingo games, etc., are all taxable income. Nonresidents may only offset gambling winnings from New Jersey sources by gambling losses incurred in New Jersey during the same tax period. " See http://www.state.nj.us/treasury/taxation/pdf/pubs/tb/tb20r.pdf
Note that the casino likely withheld tax on the winnings - if so, you would have to file a New Jersey return to get the withholding back (on the assumption that you wouldn't actually owe any tax).
