A screen recording to MP3 conversion only needs the audio track. Drop a QuickTime, Screenshot toolbar, or Screen Charm recording here and download the sound as MP3. The picture is discarded, so the file is small enough to drop into a podcast app, a transcript, or an email.
Screen record to MP3 works the same way for any other video — MP4, MOV, MKV, AVI, or WebM. If the recording has no sound, the MP3 will be silent. Record the mic or system audio first, then convert. The screen record with audio on Mac guide covers that setup, and no sound on a Mac screen recording covers the usual fixes.