They keep track of tweets that are deleted for any reason at a later stage. You can see the tweets and get additional information about them like how much time after it was deleted and what links were shared in that tweet.
The idea is not new. We already have a bunch of services out there targeting specific genre. Twitter even killed one such service claiming it breached their terms and conditions.
Politwoops already has a version for users in Netherlands keeping an eye on tweets from politicians there.