The AccountRight API is the service that needs to be running in order to connect from an external application.
To verify that the service is running, open the Task Manager and check the MYOBAPIService is running, as well as the other 3.
You may use the following link from the MYOB online guide on how to install the API, however this still has images from the version up until 2016.2 with the icon on the task bar no longer available in 2016.3 but the installation process is similar.
A way to test is by opening this URL (http://localhost:8080/AccountRight) on your browser. If it shows the company files then it can be a good sign the API is active.
If you had a previous version of MYOB installed on your computer, uninstall it and then reinstall 2016.3 just to make sure it is not carrying anything over from the previous version. Also, please go through recommendations mentioned the link above.