I'm not surprised he has bad wind if they just feed him what they're eating. Not sure introducing a balanced dog food is going to make much difference one way or the other for one day a week. If he's being fed rubbish then dog food isn't going to do any harm, surely. Poor little chap.
It all sounds a bit disastrous tbh and they sound completely clueless.
They clearly have little interest in this animal: little or no training, totally unsuitable food, little time spent with him. Why the hell have they got a dog? Also, I know you say he isn't being ill treated but leaving a dog alone for 12 hours on a regular basis is ill treatment in my book. What happens when he needs to pee or poo? Does he just do it in the house or does he hold himself for that length of time?
I couldn't bear this if I were in your position. I know they might possibly tell you to mind your own business, but could you somehow try to tactfully get across to them that a dog does not fit in with their life style? Having said that I probably wouldn't be brave enough to say anything.
Either you have to suck it up knowing that at least you're giving him a decent time once a week or you walk away. I know that's not helpful, and I know you know that already, but whatever you do you're going to feel bad.
Perhaps you should just move on, leave them to it and find another, better looked after dog to borrow. That might sound harsh, but they're going to go on treating him badly whatever you do and one day a week is not going to make that much difference to his overall life. It's difficult but this is supposed to be something that gives you and the dog pleasure, not turns you into a dog refuge.