The NPrinting API exposes TaskExecutions which returns the overall status and progress of a task execution. What is not exposed is the task execution log information. This information is retrieved on the dashboard via the following endpoint.
This endpoint doesn't appear to be integrated with the NP API because the authentication (and cookie information) appears to use a manual login and not the API login functionality.
Please add an endpoint (something like TaskExecutionsLog) to the NP API.
See the Qlik forun discussion for more information: