that's not how taxes work anymore, this isn't 1966. the rules have changed so that you don't have to pay the other taxes out of state.You have to claim the taxes based on where they are sourced (where you made the money). Then you can get a credit on the state where you live for those taxes paid.
To further expand... if you are playing in New York and live in New York thats all NY income.
If you go play a game in New Jersey. It is still all New York income, you will pay the amount owed to New Jersey for that one game and then you will take a credit on your New York tax return for the amount you paid to New Jersey.