I'm not aware of any off hand.

I bet you could make a pretty cost effective (read: cheap) setup that uses S3 for storing current state (for displays and/or "apps" to poll); and amazon lambda for actually authenticating and updating scores. Not 100% free, but.. cheap and <cough> "serverless". Even with a display board polling for updates once a minute, mostly with 302's, the S3 cost would be under a buck a month. It's a bit crude to do polling, but at tiny scale.. who cares? Just get your http caching headers correct for content you store (ie: minimal caching for index.html, long TTL for index.js.$version) so that people hitting refresh on a mobile browser don't run up the bill.

A bit more effort could reduce the bandwidth but at the expense of keeping things running (perhaps an EC2 instance) that would support either notifications or long polling. But that seems not worth the effort other than for the experience of it, unless you're building a service for more than yourself.

There may also be something useful in the tournament software out there.