Linux is a bad example. It's not "community" development by any real definition of it, because Linus controls everything that goes into the mainline codebase. If anything, it's community maintenance, because that is delegated out.
More importantly, Git by itself does not promote community development. No source control system does. Some make that style of development easier, but none of them actually directly promote it.
GitHub is not Git. GitHub is the Git version of SourceForge. Nearly all the community development features(bug tracking, forums, etc.) on both sites are built beside the source control system, and aren't really integrated directly to either Git or SVN.
He is saying that ASF would benefit from the kind of community development that git promotes as exemplified by GitHub and linux.