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If I open the index file directly from my desktop, it gives the behavior you describe, but if I put it in my public web folder and browse to it with firefox (myMachine.local/MyProject.htmld) then firefox asks me what to do with an ICS file and I can choose an app to open it or to save it to disk. So I think the issue is that you're looking at the file locally, and it won't do that if you actually post it to a web server.

If you don't have a web server you plan to post it to, then browsing the folder with Finder, you can see the .ics files in the Calendars sub-folder, and double-clicking them should open them in your default calendar app.