that's bull**** about your parents wanting to know "what other people are typing to him". you're just a nosy sob that wants to know what his brother says/knows/is told. i know because three years ago i did the same thing to my little brother, and then i realized how petty i was being, and i quit.
also, to my knowledge, there's no program that can log what other people type... unless you somehow hack into the SC engine. there's ways of setting up bots to follow your brother into various channels and log every word that's said within that channel (what your brother says, what people say to him, etc.) but that wouldn't work once he joins a game, because the bot wouldn't follow him into a game.
a keylogger would work, to tell you what he's saying, but the easiest way to find out what people say to him is to get one of those keyloggers that takes screenshots every number of seconds (like, every 10 seconds, for 2 minutes after the last key's pressed). there's tons of those... do some research on BOTS.