What refund are you referring to? Gambling winnings are entered as income and you won't get deductions for it unless you are filing a Schedule A where you will enter your losses up to your winnings in the Other Miscellaneous Deductions section of your Schedule A. Everything should flow to your State tax return.

I am getting a refund even with the W2G reported (so I had a refund, entered the w2g and watched federal and both states reduce the refund). Now when I go into my nonresident state filing and fill out the Income Allocation, I put in other income for that state and another deduction to the refund.

Make sure you are not double counting your entries. Ensure you don't have your W2G on the state return already before adding your W2G income again on the State return.