No you shouldn't have to go over. People should be brought up to know how to behave when eating out.
I agree with the second sentence, and I wish all parents would do that. However, given that not all parents do, let's look at the logic of your first sentence. Giving him the benefit of the doubt, let's assume that the man in the OP wasn't properly brought up and doesn't know how to behave when eating out. He reaches adulthood blissfully unaware that watching TV with the volume on is annoying to other diners. He goes to restaurant after restaurant doing this, and no-one ever says anything, so his belief that it's OK is reinforced. He rarely notices the glares and stares of his fellow diners (he's glued to a screen, remember) so he has no idea his behaviour is objectionable - if he does notice them, he thinks it's their problem. And so you get the normalisation of what almost everyone on this thread has agreed is rude behaviour. If, however, every time he did it, another diner or a member of staff alerted by another diner asked him to turn the volume off, he'd soon get the message.
I really can't understand what the problem is with asking someone to stop disturbing others. I do it all the time, and because it's unusual I do sometimes get a grumpy or astonished response, but mostly people comply. Only very rarely is someone rude or aggressive to me, in which case I go to a member of staff. Here's the most likely scenario had the OP said something:
OP: Would you mind either using headphones or turning the volume down?
Man (grumpily): OK, if you insist.
Job done. Any refusal, alert the staff. Or if anything in his body language or demeanour suggested aggression, go to the staff in the first place. Why is that so hard?