It depends. If your overall tax liability with your gambling income and itemized gambling losses result in lower tax liability, then yes, you would get a refund. If not, then no, you would not get a refund. The taxes withheld on the W2-g are treated like any other taxes withheld. They are added in with all your other taxes withheld and applied to your overall total tax liability.
In MO to claim your gambling losses you will need to itemize your return. MO only allows you to itemize your state return if you also itemized your federal return. If you do not itemize, you cannot take any sort of deduction for the gambling losses.
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