This seems like an out-of-control sibling rivalry. It's clear that Aaron has to be top dog all the time, and he can't bear to share the spotlight with Nick. Rather than gaining confidence from his Debate Team success, he feels the need to constantly outshine his younger brother. Aaron probably feels threatened by Nick, and deals with this feeling by wanting more and more approval from teachers, friends and his parents.
Aaron needs to understand that his younger brother has the right to excel too, and that if Nick does something well, it doesn't reflect badly on Aaron. Instead of trying to beat and humiliate Nick, Aaron could help his brother become an even better chess player, and stay away from the Chess Club because he already has the Debate Team.