I hope so, clicking on 'sign in' logged me into my github account with no further action. Does anyone know how they did that?

You're probably already logged in on the main Github.com domain.

You were redirected from the community domain to the main domain to log in. Once there, the system saw you were already logged in and redirected you back to the community site with some proper tokens in the url to identify you.

But they're different domains; how are they identifying me as a client?

github.community isn't. It sends you to github.com regardless, since their login is there. github.com sees you're already logged in, and redirects back, passing auth.

That suggests it’s bypassing OAuth—with OAuth you’d get a “GitHub Community wants access to X, Y and Z” interstitial.

Most OAuth providers have a flag for first party clients which allows them to bypass the usual authorization dance and just bounce you straight back to the origin.

Unless it's by the same authors as GitHub, and has access to the same OAuth client id/secrets as the master GitHub app.