Forums, in general, remove all concepts of time period. Posts can be separated by short or long periods of time. Besides the 28 day thread marking timeout I am unaware of any time based information kept track of. As opposed to the awstats my hosting provider gives me where I can see activity vs time.
I do understand that in many respects the random people listed idea you have (and also agree with) is similar.
A query is scheduled to run against the database to determine the most active users in the previous 28 days. These users go on the leaderboard.
The query could be scheduled at midnight, hourly, or even every 5 minutes if you were that way inclined.
So, who was the most active between 9:35am on the 2nd September and 9:35 on the 30th September?
then run it again at 9:40..