It depends.
I won a taxable jackpot at Oaklawn Park in Hot Springs, Arkansas.
To my shock, they required proof of my SSN.
I assume the same applies to the only other legal casino in Arkansas, the dog track.
I protested, of course, but it did no good.
If I remember correctly, he said they would accept anything with my SSN, such as a Medicare card, which I didn't have at the time.
I dug around and finally found my SS card, went back and collected my money.
Mississippi doesn't require proof of SSN, but they do take out state tax from winnings.
Edited to add that Arkansas also collects state tax from a jackpot.
Not too big of a deal, except you must file a state tax return for every state in which taxes were taken from a gambling jackpot if you wish to re-coop some of it.