On a public form, when the initiator is public (not an authenticated user), the initiator value shows as "Anonymous User". So it will not be able to email them that way.

You would need to include a field on the form asking them for their email address and send them email using that field variable as the recipient address instead.

That's assuming you are just sending an email.  Your screenshot is actually from a User Task, which won't be possible to assign a task to them to complete.