However the calendar file gets created out of thin air from the GET parameters alone. There is no state or storage involved. Other calendar apps have a backend with a DB; this one doesn't. Now whether that counts as truly serverless is up to you I guess. It's as close as you could get with a calendar I'd say. Not easy to get the point across in a title. ;) Hope that helps.
FTFY
The key part of serverless is that you don't have a server idling around. Whether or not you use a hosted db is not relevant.
> Now I can finally send my friends a link to a calendar event for our next pub crawl.
I suggest you update the tagline to say "link" as there is no "terminal" involved. That is, you don't use cURL and you don't send a normal calendar invitation email, but instead you send a message with a link that gives them the ical file when they click it.