What were they playing for on this one?

i suppose in the third film the ducks played not only for respect but also for education as well. since the ducks had full athletic scholarships, they had strict limitations based on how well they did on the ice, which affected their placement in the school. if they lost every single game they would be kicked out of the school for lack of performance.

also i think they were playing for the respect from the people in the school. theyre the MIGHTY DUCKS. they had to live up to their reputations. and i guess it was for their own pride,

the movie took place in a prep school which was basically high school for rich ppl that would later prepare them for college.

No. In the first film, they played for fun because thats what Bombay told them playing hockey was about. In the second, they played for pride, because they were representing their country and McKay taught them in class that olympic teams in history played for pride. So, in the second, they played for pride because they learned to play for fun before that. In the third, they played for pride and respect. Orion taught them how to work for pride, then taught them a new style of hockey in order to beat the Varsity team and gain respect from others and recognized as the true symbol of Eden Hall.
Eden Hall was high school, not college.