Actually I just got it to work in Outlook.
How did you add your calendar? I originally clicked the public link, downloaded the ical file and opened it.
But there is an option in outlook to add a calendar from the internet using a link. When I did that it worked like I would expect.
It looks like there is similar method for adding calendars in Google Calendar. I just tried and it brought in existing events, but I don't see a way to force a sync. I'm not seeing new events added after the calendar was synced initially