A directory submission is a process of submitting URL to various web directories either to do it manually or by automatic software. All directories submission form has email column which is compulsory in all cases. So you need email ID and domain email works better as directory editor have confident that submission is genuine. Now the question it that why it should be separate valid email the reason are:

When you submit to directories there is most likely that your email will be spammed as thousands of submissions will expos? your Email ID.

Some directories also publish your Email ID along with listing and more chances that your email will be in spammer list.

When ever site is submitted to directory in most case they first send auto responder for submission thanks and followed by other mails which will fill your Inbox.

Some web directories send confirmation email to verify the authentication of submission and separator account is helpful for staff or outside submission company to handle such verification. Since it is not your business or personal email ID you can give it to out side submission company for working.

Few Web directories require account creation and process involve verification of email and account. Separate email account is helpful for staff or submission company to handle such account creation without accessing to your personal or business email account.

You need valid email ID to receive communication from directory editor regarding approval or rejection of your site.

So you must have separate valid email ID either of your own domain or on some free email provider i.e Yahoo, Gmail, Hotmail etc. In case of free email provider tried to have your domain in email to give confidence to editors that submission is genuine.