After emerging gentoo-rsync-mirror, the config file /etc/rsync/gentoo-mirror.conf contains a wrong directory name (/opt/gentoo-rsync-mirror/portage). This will break running /opt/gentoo-rsync/rsync-gentoo-portage.sh because the script will try to create a new directory in /opt/gentoo-rsync-mirror, which doesn't exist, since the emerge installed the package into /opt/gentoo-rsync.
Fixed. Thanks for your help.