What is the command that replaces 'drush variable-set'?
Following some more research it seems the new command is:


drush config-set &lt;config-name&gt; &lt;key&gt; (where the old format was drush variable-set &lt;name&gt; &lt;value&gt;). Alias: cset.


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: contact.form.feedback recipients, update.settings notification.emails and system.site mail.

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
'update.settings:notification':
  emails:
    - admin@example.com
  threshold: all


to update this you need to run:

drush -y config-set update.settings notification.emails.0 admin2@example.com


Source: Leverage Drush 7 for Drupal 8.

Note: Drush 7 no longer supports Drupal 8, but this still applies.