I am not sure that the satoshidice will return the money back, because this is a long-standing problem and has just been reclaim again. We don't even know the proof, whether @OP received the deposit at the time or not, even he only gave a tx address to track the deposit.
And maybe the satoshidice has also lost its user data, so this will be difficult to verify the case. But better, this case was transferred to the reputation section.
And from what i remember if your bet wins they send the money back plus the profit, but if the bet lose then you don't get anything back.
Satoshi Dice and other similar gambling sites of the time responded with a payment to the originating address to acknowledge the transaction, whether the bet won or not. There is no corresponding acknowledgement to the transaction linked in this thread because the game was shut down about a week prior.
The owners of the game rebranded as MegaDice in 2017. They may still have ownership of that address.
I tried to track the BTC @OP ending at this address, and this address was active the last time in August, possibly the old owner was no longer active.
https://www.blockchain.com/btc/address/1dice97ECuByXAvqXpaYzSaQuPVvrtmz6