Not to mention, Elixir is a joy to code in, and a lot of us are still experimenting with it, trying to figure out where it's going. So projects like this are a good outlet.
Not sure if Trello itself requires it or benefits from it, but any distributed system can benefit from this architecture.
As for the benefits of using Elixir, I'm not qualified to answer that since I've only skimmed the surface of what Elixir is (but it looks intriguing!).
And finally Meteor has it with utmost simplicity as well. Just save to the database and Meteor updates the data to everyone, automatically.
Joking aside, I wonder if it's possible to write a real-time webapp with C and CGI. Ok, 'possible' is a strong word; but I'd really like to hear from someone who'd given this a try.
Now, would I deploy it for production? Not likely.
I don't recall seeing one written in C, I think the last time I saw a CGI script written in C was a some years ago version of Nagios