Apartments have apartment numbers, so different apartments would constitute separate billing/shipping addresses. For multiple people living in the same apartment/house (i.e. roommates at the exact same address), they may be SOL.

Edit: Although, on second reading, the address check may only be to prevent multiple entries per account. Emphasis mine:

Multiple registrations from any Steam account holder will be void.

We will use information such as shipping address and/or payment information to eliminate multiple entries.

Those restrictions could be done per account, so multiple Steam accounts at the same shipping/billing address might be fine as long as each account has different payment information (i.e. the accounts don't have the same owner name and/or credit card). Could still be an issue for someone trying to register a whole family at the same address, if all the accounts are using Mom's credit card.