That cable looks like an old Centronics Parallel (NOT Serial) cable for a printer. If you go to google images and google Centronics cable, I'm sure you'll see it's the same.
@@axelthefoxytechworld8024 or maybe it used a small receipt paper printer or something that would print out the time and date of each message that came in. That long ago I'm positive they wouldn't have had the technology to have it print out what they were saying because voice recognition wasn't there. So I'm guessing it's a printer for diagnostic purposes or like I said maybe it lists time and dates of phone calls missed. Again, just a thought