Call Waiting is the signal that's delivered during actual call to inform user there's another call waiting. There are various method how to deliver such signal thru POTS line. To work correctly, the format used by exchange device (ATA192 here) must be supported by particular phone connected.
Based on the sound you disclosed I assume the ATA192 is configured to use polarity reversal (two clicks) followed by DTAS followed by Type II caller ID digital info (it sounds like Bellcore FSK or ETSI FSK kind, but consider it blind shot, I can't reliably identify digital format by naked ear). Compatible phone should mute them and take appropriate action based on data received. Your phone seems to recognize neither polarity reversal nor DTAS as special signal, thus it do nothing and you hear digital transmission as is.
