You're the second person to mention this, and I would like to know: Why you don't think this is a game?
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There are books on what is a game and what is not, but I think that the book that got the deeper meaning is: The Art of Game Design: A Book of Lenses.
In the book, the author define game as “a game is a problem solving activity, approached with a playful attitude”.
What you missed is the "problem solving activity".
The most similar game to yours that I can think of would be Viridi, but there you need to water your plants once a day and plant seeds: even those very small activities create a problem to solve that engage the player more deeeply.