I run the Zattoo app on my Google TV streamer without any problems. I assume that your problem probably has more to do with your Internet provider / connection and specifically with the IP address assigned to you (geoblocking). Which internet provider do you have and does it use CGNAT? Test this with a site like https://wieistmeineip.ch. What country is displayed for your IP address?

I have a similar problem with the Sunrise TV app. The Google TV Streamer doesn't seem to support all apps or they can't be installed for strategic reasons. Very annoying.

I no longer have the streamer in use, but I would like to try resetting it to the factory settings:
In the settings, go to System > Info > Reset to factory settings.