Anonymity is the major reason why many prefer Bitcoin. Maintaining it in the e-Wallet is completely anonymous. For instance, depositing and withdrawing through Bitcoin eWallet is anonymous on its own, but in a really great Bitcoin casino, the process of signing up also is completely anonymous. Sites with features like these are the ones that attract many players. Cause gambling is still illegal at some countries, so this is the best feature to free gambling.
Maybe it sounds funny but I think game Dice is the reason of why bitcoin gambling become popular, I haven't seen any dice which uses usd for playing. I think anonimity don't plays important role because gambler don't has to hide anything and also in most countries gambling is absolutely legal. Bitcoin gambling is easy and you can withdraw money at any time you want and any amount that doesn't exceed number of bitcoins available in hot wallet (that's usually higher than 10 btc). So no need to waste time in verification, no need to wait for payment confirmation from casino and etc.