For NC state, "Nonresident Income Allocation" section, do I enter gambling income as a negative amount for "Other Income/Loss on Federal Return" since I have a net loss?

No, because you cannot have a gambling loss on the Federal return since gambling losses can only be deducted UP TO the amount of your winnings.

I'm asking about the entry on the North Carolina state returns.   Because I have a net loss, how would it be counted properly on my NC state taxes if I don't enter it as a negative?   When it says "income/loss", that seems to indicate a loss would be a negative.