Hi,
Is your live website accessible to anyone ?
If you've activated the "site offline" setting of the Joomla configuration, then the only way to access the frontend of the website is to login with a super admin access.
And thus, when you reach the checkout, you're already logged in and thus the "login" area doesn't need to ask you your email address as it already knows it.
I suppose that the situation is something like that and so you don't have to worry. People who are not logged in will be asked their email address on your live website.