That would be correct seeing as the ping command will only ping the network interface that the service is running on. (your network card)
Anyway, NZBGet supports API calls. Have a look at the documentation here: https://nzbget.net/api/
and in particular the status method: https://nzbget.net/api/status. I don’t know the specifics but i guess this will be your only way for home assistant to communicate with NZBGet.