Figured out a nice semi-onliner for this. Once this runs, you still need to move it out of /tmp/ to wherever you want to store it.
sudo -H -u mattermost bash -c '/opt/gitlab/embedded/bin/pg_dump -U gitlab_mattermost -h /var/opt/gitlab/postgresql -p 5432 mattermost_production > /tmp/mattermost_production.sql'