Doing some background reading on this topic, I don't think there's any way to "publish" a GPE Calendar directly to Google Calendar. That's what Erminig is for - it acts as the intermediary. However, thanks to Google Calendar exporting a standard ics file to a url link, it's possible to connect it directly to a Subscribe link in GPE Calendar, and that serves the useful purpose of creating a one-way transfer with minimal work for a lot of people.