Assume you get the winner right. If W is how far off you are from the winner's score, and L is how far off you are from the winners score, it looks like "delta" is 2W + 2L if you were off in opposite directions (one too high, one too low), and W + L + |W-L| if you were off in the same direction (both high or both low). That seems reasonable.
In other words, you always have "bad points" equal to the sum of W and L for the individual teams. For the spread, you either gain "bad points" either to the sum of W and L again, or to difference between W and L. Harder to say than it is to do, but the mathematical logic of that is fairly simple and elegant.
This way, if the real score is 31-10 and the predictions are 34-13 and 34-7, both guesses were off by 3 for both, but 34-13 has a better delta because his spread was correct and so he has a delta of '6', whereas 34-7 has '12'. So the tipping point where getting the spread exactly right wouldn't be enough due to going way over the total points is that 37-16 would be an equivalent to 34-7, but 38-17 would be worse.
TL/DR formula seems reasonable.