The checkout form by default will give the user the option to login, or register as a new user. You will need to restore this portion.
If the user is not logged in when they get to this page there should be a link to login, it is this link that the user will need to make use of. The form fields that are there are to do a quick registration for a new user if you are not registered already. So the error you are getting is correct as this is not a login form but a new user registration form.
I'm including some screen shots of the page in both states so that you have a reference.