On one of the older routers you can reset the DNS servers and get your client to refresh the DHCP lease to pick it up.
On the Internet box that’s not possible and you’d need to assign DNS servers on the clients. Swisscom presumably make this hard to mess with on the Internet box so Swisscom TV can rely on using the Swisscom DNS servers in case we, the customers, accidentally break stuff we don’t understand.
If you don’t know how to do these things it’s probably better not to mess around.
Which is ironic since Swisscom DNS is historically hugely unreliable. The Google servers are more reliable because if they break someone actually cares and fixes them. It’s clearly quite unacceptable to leave this broken over the weekend if they’ve removed the facility to change it on the Swisscom Box. The TV box is immaterial, if it needs a particular DNS server there’s better ways to force that and it’s pretty dumb to mess with DNS like this anyway unless a) they’re real sure what they’re doing and b) prepared to fix it when it (inevitably) breaks.
Score, about 2/10