Caveat: I don’t really play a lot of video games
But hear me out!
When you learn a piece on the piano, you are being invited to participate in someone else’s art. Most of it is written out for you already, but you still get to make your own choices and your own discoveries along the way.
Not only that, but to get through the piece, you usually have to practice some new skills and ‘level up’, as it were. These new skills may not useful in other aspects of life, but using them means you aren’t being passive in your downtime. You aren’t simply watching or listening something, you are helping to create the story, the song.
Also, if you do either for excessive lengths of time, you are likely to have sore hands.