I should have been digging deeper first. The solution came from this related Topic
that is because the service is called teamviewerd and not just teamviewer
.
sudo systemctl start teamviewerd
enables the service and likewise opening a teamviewer session.
It does not quite work as expected though. You only use remmina to start an external TeamViewer client, not running inside remmina (which is what I had expected). Anyway it works even though you can not take advantage of having the TV user ID of remotes to be stored in remmina really (which was the thing that I found appealing)