I am not a PDQ expert; I have only read the system and never gotten to play it. This, of course, makes me the perfect person to answer your question on how damage directs the story.
In a lot of games, after you take some amount of damage you start taking determents to your skill use. Ex, “You have lost half of your hit points so all of your skill checks are at -2”. In PDQ you apply damage directly to your ‘qualities’ but you apply the damage individually and not globally.
So, say you have qualities like “Master of the Blade (+6) Expert”, “My Man Godfrey (+2) Good”, and “Socialite (+2) Good” as qualities and you get into a sword fight. When you take a level of damage you have to apply it to one of these qualities. Because you are in a sword fight you probably don’t want to reduce your Master of the Blade quality so you choose to have either your butler Godfrey take a hit (reduce the Quality for Godfrey actually) OR reduce your Socialite quality. The choice is up to you but whichever you choose to take the first hit signals the GM that that is what your next scene/encounter/adventure should hook on to. So if poor Godfrey takes the first hit then the next adventure should have something to do with him.
That is how I believe that ‘damage helps create the story’. It more guides than creates.
Mitch