We have older kids too, but video games were definitely something we had to manage. We took a similar approach in allowing them to "earn" time. This included chores, but also process based check marks for school. Meaning, it wouldn't be awarded for grades, but for keeping their work organized, getting extra practice, reading, etc. As far as the rainy day is concerned, I think it's fine to let them get some extra time.
One thing that does concern me as a parent regarding Fortnite is the online aspect. That wasn't as prevalent when our kids were young. I have played the game myself, and while I have not personally witnessed any really bad behavior, you do have adults communicating with young children on a regular basis. That does not make me super comfortable. There is also the foul language issue if that is a concern for you. It's possible to play the game without a headset, but verbal communication is a big part of it.