Indeed - if they have a esp inside you can just supercharge it and benefit from all the possibilities that esphome offers 
I would expect your internet box to be powered by a (maybe 12V?) PSU that doesn’t even use a ground pin 
You could also think of a DIY ~$3 setup like this and (because it’s always on anyways) even just use it to switch the DC line:
Wire it using the NC contact will even save some energy as the relay is not energized always then but only when disconnecting the load 