score:5
UNICOCAMPANIA consortium includes 14 public transport companies:
AIR, ANM, BUONOTOURIST, BUSITALIA Campania, CIAV, CLP, COSAT, CTP, DAV, EAV, SITA, TRENITALIA, TROTTA BUS SERVICE, AUTOLINEE CURCIO, AUTOLINEE EREDI ARTURO LAMANNA, ETTORE CURCIO & FIGLI, FRANCESCO & GIUSEPPE MANSI Snc
It seems that with Napoli card you can only travel around Naples city and suburbs. But you can buy a Tutta la regione Card which costs 11 Euro more and then you can travel all around Campania (including buses on islands Procida and Ischia, but not the ferry to them!) except Vesuvio for which you have to pay 2,70 Euro one-way.
BTW on page that you linked, there is a link to pdf which explains on the first page what area you can travel with this ticket.