This is a hard one. No it is not your job - that is his job and his only.
I do turn the TV off and pack away the toys during the goodnight phone call. I usually play quietly with one of my girls whilst the other is on the phone. I try to cut down the distractions.
I don't force them to stay on the phone any longer than they want to. Sometimes they just want to say Goodnight, ILY and hang up.
Unfortunately he does not reciprocate - he has the TV blaring in the background and plays noisy games. Or worse he makes them do the phone call alone in their room (like punishment - yes, he is a dickhead).
If my girls are really engrossed in something I don't pack it away. I do turn the TV off and I do ask the other child to be quiet whilst her sister is on the phone to be considerate.
I don't do any of this for the sad clown or to help their relationship with him. I do it to so they can choose to either talk to him at length or not. And also because they are so little. When they are older it will be up to them to find a quiet place just like they would for any phone call.
He doesn't get to bitch at you anymore and you don't have to listen to it. If he is bitching at you I would say you might need to ramp up the NC. Don't discuss this stuff with him.
I would consider turning the TV off but if your son is old enough to find a place for the phone call himself then I would ignore this issue completely. The kid is choosing to talk to his father whilst watching TV. Not.Your.Problem. If the roles were reversed and my girl were older I wouldn't take it up with the sad clown - I'd take it up with them.