You should use Method 2. As long as no state or local income taxes are withheld, which would show up in Boxes 15 and 17, you are better off leaving all state information off your W-2G.
Please keep in mind that if you do go out of state to gamble, you may be required to file an income tax return and pay taxes to the state in which the casino is located, even though Texas does not assess a tax on gambling winnings.
@mamiamjo
