Yes, you will pay state income tax on gambling winnings won in the state of Louisiana. You need to file a non-resident Louisiana state tax return. Your state of residence doesn't matter. The requirement comes from the state where the earnings came from.
Louisiana Department of Revenue website states "Gambling winnings earned in Louisiana is considered to be Louisiana sourced income. A nonresident who received gambling winnings from Louisiana sources and who is required to file a federal income tax return must file a Louisiana return reporting the Louisiana income earned. If the amount withheld is overpaid, a refund of the difference will be issued or credited to the tax liability for the following year, based upon the taxpayer's return."
