What is there to understand? don't you send a bet to a Bitcoin address? the betting system relies on Bitcoin network only. The satoshidice.com frontend website serves only to see some stats and to copy down the betting address, which is also available elsewhere like blockchain.info
Right, so your explanation is that people typically write down their favorite Bitcoin addresses and monitor the blockchain for the outcome. I would have expected S.DICE was a more mainstream thing for impulse gamblers,
as in find satoshidice.com, buy bitcoins, bet them, repeat.
But what we are saying is that once you find satoshidice.com and bet, the address is saved in your client and you can keep doing the repeat part without going back to the website.