After you file

TurboTax asks if you made money in any other states, which is where you can enter your other state (it is embedded in the Personal Info section).  TurboTax also asks if you had state withholding that is indicated on any of the forms (W2, 1099 etc).  

Virginia requires you to file a nonresident tax return if you Virginia adjusted gross income is $11,950 if Single or married filing separately or $23,900 if Married filing jointly.  

Your gambling losses are an Itemized Deduction so you will only reduce your gambling winnings if you itemize.  Virginia allows itemized deductions if you itemize on the federal return.

After you complete your Virginia return, you can apply any taxes paid to Virginia to your North Carolina resident return as a credit.