Does it mean that the new traffic predictions, as well as the
    increased waypoints limits, are not accessible via the JavaScript API
    except for Google Maps for Work customers, but they are accessible to
    the general public via some other API?

It appears so, but they state "for now" so I'm guessing it will be available (hopefully) soon.

    What is the non-JavaScript Maps API?

There are Java and Python client libraries: https://developers.google.com/maps/web-services/client-libra...