There’s a subgenre of traditional roguelikes known as “coffee break roguelikes”. These games are specifically designed to be highly compressed experiences without sacrificing the characteristic difficulty of the genre. They happen to be a perfect fit for this sort of daily game. I’m not aware of any that actually do this though!

The roguelite Spelunky HD has a daily seed with a leaderboard. That game can be finished in 10-15 minutes (if you’re really good)!