They don't. That's why if you send a wager from a hosted (shared) E-Wallet, you lost your bet. (Or at least, the payout if you did win will go to someone else's wallet).
Since a Bitcoin transaction has INPUTs and OUTPUTs, SatoshiDICE looks at the INPUT (or chooses one of the INPUTs if there are more), and uses that for the payout address.
It works if you have your own wallet (Bitcoin-Qt, Blockchain.info/wallet, Coinbase even) but it doesn't work if you have a hosted (shared) E-Wallet.
Many coins have been lost by those wagering due to this.