I think, you are supposed to tally.
If you win 7 to 5 prestige you add the difference of 2 to your score. Or am I mistaken?
Maybe I'm not understanding the official campaign rules, but as I read them now: both players tally their individual scores (whether winning or losing) from game to game... first to 13 overall (campaign) prestige w/o going nuclear wins... which (again, as I read it) would mean both players could reach 13 campaign points at the exact same time. For example, if US was ahead 10 cp to 8 cp, and USSR won the next game: 5-3. Which is still fine imo.... just play a final tie-breaker.
That's my take (my variant aside).