That title is highly editorialized. The actual effect is just that .eu domains will have to be renewed through a registrar that's established in the EU. Most major registrars probably already fulfill that requirement, and those that don't shouldn't have any problem with founding an EU subsidiary.
EDIT: Missed the part where "Accredited
.eu
Registrars
will not be entitled to process any request for the registration of
or for renewing registrations of .eu domain names by those [UK] undertakings, organisations
and persons." Still, I bet the vast majority of domains will be transferred to some shell entity in the EU, even if it's just domain owners selling off domains they can't renew anymore.
.eu domains are restricted to EU, Norway, Iceland
or Liechtenstein residents and organizations[1]. By leaving, UK residents and organizations not established in one of those countries lose the right to register or renew a domain. Plus, even existing registration can be summarily revoked by the Registry.
EDIT: Missed the part where "Accredited .eu Registrars will not be entitled to process any request for the registration of or for renewing registrations of .eu domain names by those [UK] undertakings, organisations and persons." Still, I bet the vast majority of domains will be transferred to some shell entity in the EU, even if it's just domain owners selling off domains they can't renew anymore.