Chapter 2 and 3 of the "BGB" contain several paragraphs which define legal rights and obligations for doing business via the internet or telephone.

§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.

Sure, they're not following the rules. Why would that affect the validity of your contract with them if you purchase good from them? Why would this contract not bind the seller?