It means everything. Banker has to take extra care to ensure the regions are fed if the enemy burns/steals the food, the judge has to deal with nobles captured in battle and infiltrators, and the Ruler has to balance the sides of the war to try and keep the odds in his favor.
Other than the judge, its simply the job becoming more important but nothing changing really. Ruler's diplomacy and ability to run the realm well becomes more important, but was already important. Regions being fed should always be a priority, just a higher one when at war. I am not saying that it doesn't become more fun when at war, but I don't see why it would be fun at war for banker and ruler, but not fun when not. The general not being fun when not at war is for obvious reasons, and I can see reasons for saying the same with judge.