It's not. Read the documents linked to from the article. The law clearly refers to certificates with domain names in them, not client certificates. Actually the bigger impact of this seems to be that you wouldn't be able to host websites anonymously anymore, making WHOIS privacy meaningless, because the law appears to mandate that all certificates contain legal identities in them.
Annex IV:
Qualified certificates for website authentication shall contain:
(b) a set of data unambiguously representing the qualified trust service provider issuing the qualified certificates including at least the Member State in which that provider is established and:
—
for a legal person: the name and, where applicable, registration number as stated in the official records,
—
for a natural person: the person’s name;
...
(e) the domain name(s) operated by the natural or legal person to whom the certificate is issued;
It is interface between webservice and member state for sending authentication data to member state for purpose of auth. Think OAUTH so webservice does not have to save any auth data.
Annex IV:
Qualified certificates for website authentication shall contain:
(b) a set of data unambiguously representing the qualified trust service provider issuing the qualified certificates including at least the Member State in which that provider is established and:
—
for a legal person: the name and, where applicable, registration number as stated in the official records,
—
for a natural person: the person’s name;
...
(e) the domain name(s) operated by the natural or legal person to whom the certificate is issued;