Technically, any numeric attribute can have a leaderboard defined on it - and not only the ones from the scoring system.

However, to keep things simple for app developers, we only support the pre-defined leaderboards as of now.
This allows the app developer to focus on only the core loop of the game/app and submit only the relevant scoring updates (either directly to the profile scores or as part of challenges). The developer doesn't need to worry about updating leaderboard along with the score.

That said, we're working on allowing the app developer define custom leaderboards which work in pretty much similar fashion - that is, the app developer should worry about only updating the relevant attribute and not bother about separately updating the leaderboards. But that feature is some time away from release.