For the same reasons you might engage in any entertainment activity.
Real-life still-unsolved puzzles are hard ; whereas puzzle games keep the difficulty under some control (except for the infamous boat puzzle in The Witness).
Real-life problems are hard because, often, proper domain modeling/formalization is part of the problem. Puzzle games generally don't have this 'domain modeling' part, they provide you with an extremely consistent set of rules, and you have to build a solution inside it. Sometimes this set of rules is partly implicit, and discovering it is part of the fun (e.g The Witness, Antichamber) ; but you never have to worry about the real-world and it's complexity.
Not every puzzle game has mechanics that combine in such surprising and entertaining ways so consistently, but I think this feeling is what most of them are going for.
The one type of single player game I do play are either city building games or 4X games. The freedom for creativity and randomness, respectively, makes every game new.
I do think you're on to something in that having to visualise everything yourself when reading books does get me more invested, probably because I can better project onto the characters than if they're just given to me on a screen.
I recently played an interactive visual novel (think choose your own adventure only digital) and.. wow, it was not as I expected. By the time shit went down, I was already so invested in the characters that by the time shit hit the fan, I actually legitimately cared about what happened in a way that no movie or show ever has and only a few books and games have.
How do you feel about the highly interactive "all of your choices will impact the story" games, where few people will experience exactly the same thing you did? For example, Detroit: Become Human or Until Dawn, where any or all of the main characters can die without the story ending (quite early on in some cases too; but they can also survive), or the Life Is Strange games?