[swhitt]

The reason why SatoshiDICE can do this is because they include the output of the bet transaction as one of the inputs to the win/lose response transaction.

If part of the bet transaction is doublespent there's a good chance it won't make it into a block. If the bet transaction doesn't make it into a block, the response transaction won't either and is therefore worthless.

[ewillbefull]

Nobody can cheat SatoshiDICE by double-spending and spending their response transaction, because the transactions are chained as you say. But this isn't the kind of attack they're worried about.

If you broadcast a transaction and SatoshiDICE responds with a YouLoseTx, and you have built a block containing a double-spending transaction, if you "lose" you can broadcast your conflicting block. You wouldn't need much hashpower to do this and still remain positive. It's called a Finney Attack. https://en.bitcoin.it/wiki/Double-spending#Finney_attack

This is why they only immediately respond to smaller bets.