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Better privacy. Even admin won't know your email.
Whether a site requires one's personal information to play is not related to whether the site requires users to register or not. For example, both bustabit and Primcedice require users to register in order to play but neither require any personal information–including an email address. Conversely it is also conceivable for a site to require users' personal information in order to play but not to require registration.
Assuming a strong password and proper password storage (salted and hashed in sufficient iterations), the risk of an attacker successfully gleaning one's password from a breached database is fairly low. And if one does not reuse the password across other sites then the site operator cannot inflict any damage by stealing the password either.