As far as I understand German law is very flexible about what constitutes a valid legally binding contract.
§312f for example defines that customers must receive "a copy of a contractual document signed by the contracting parties in such a way that their identity is identifiable" (translated via DeepL).
A simple mail address is not an identity in German law, especially not when doing business with B2C as you always have a 14 day period to cancel your order (except for downloads and various, special products).
edit: If you want to cancel, you must be able to do so via (offline) mail, too.