I don't know that much about audio sidechannels so I don't know how realistic this would be, but my immediate thought is whether this can be extended to extract not just a single key but other data as well. For example, if you had a phone next to a computer that was reading and displaying a text file that contained confidential information, or perhaps reading values from a database, could it be possible to leak the actual data this way?

I also wonder how many videos and audio recordings made near computers have encryption keys and other sensitive data hidden in them, just waiting to be decoded. Or whether a video recorded by a smartphone can reveal what the phone is doing in the background. A terrifying prospect.