Can I offset my gambling winnings from my resident state (NY), with gambling losses from another state (NJ)?

 Your gambling losses are federal itemized deduction on schedule A.   You may or may not benefit based on your other itemized ductions and your overall tax situation. 

Then for your New York State return, you will either use your federal itemized deductions plus certain state adjustments, or you will use the New York state standard deduction.   Because the New York state standard deduction is higher than the federal standard deduction, some taxpayers  may itemize on their federal return but used the New York state standard deduction. 

 The net result of all of this is that if you itemize your losses on your federal tax return, and if you use your federal itemized deductions as your state itemized deductions, then you will get a deduction for your gambling losses even though they occurred out of New York State. 

However you handle this, for both the federal and New York tax returns all gambling winnings and losses are treated the same, no matter what state they are from.