Well, there are these things called computers, and they’re really very good at this stuff. It’s not exactly rocket science (heh) to write a program to listen to an audio stream and mark and log every occurence of something else than background noise and ambient wind sounds (if Martian winds are even loud enough to make sound). Everything else that the rover has to do automatically is way more complicated.

It’s pretty likely that the entire stream of silence isn’t being stored, or sent to Earth, only the interesting parts. There isn’t any way for people to listen in real time anyway, because communications (can) only happen at specific times of the day. Every interplanetary mission works by sending a preplanned sequence of commands one day, then coming back the next day to see what the probe/rover/whatever sent back, then planning the next set of commands, and so on.