The state withholding is prepayment of state income tax, just like the state withholding from your paycheck/ W-2. The withholding at the real estate closing is not the actual state tax due on the capital gain, it is only an estimate.
At tax filing time, you calculate the state tax on all your income, then subtract the withholding to see if you owe more or get a refund.
So, no, the state tax withholding is not a deduction, from the selling price, in determining your capital gain. It is a separate transaction from the real estate sale.
Withholding
