Following some more research it seems the new command is:
drush config-set <config-name> <key> (where the old format was
drush variable-set <name> <value>). Alias:
So I'm not totally sure that I have this right (so comment and/or another answer from someone who does would be great...), but it seems that the config that includes emails are:
update.settings notification.emails and
This update is the result for some good discussion (below).
Note that some settings are arrays (rather than strings):
www/drupal8# drush config-get update.settings notification
to update this you need to run:
drush -y config-set update.settings notification.emails.0 email@example.com
Source: Leverage Drush 7 for Drupal 8.
Note: Drush 7 no longer supports Drupal 8, but this still applies.