You could probably make a poptarts are sandwiches alignment style thing out of this.
Basically, any video game with an explicit goal, or set of goals is just a puzzle game with extra steps.
What buttons do you push, when do you push them, what does this accomplish, how does that lead you to your end goal, etc.
You could even argue that multiplayer tactics constitute a puzzle, a more social puzzle.
Yes, this is reductive, but this is a dumb showerthoughts post.
The cookie clicker could still be a puzzle as long as you make it impossible to win without using some power-ups because you’ll die sooner of old age. That’s assuming there is a win condition in it. Other clickers are genuinely not puzzles since they’re infinite and not winnable. Not winnable makes them not solvable so they can’t be a puzzle.
I’m pretty sure cookie clicker has no victory condition, it just goes on and on. At least it was that way last time I played it. Things might have changed since.
There’s some kind of stock market mini game in there now, so you can play and lose at something in the game, but no overall win conditions im aware of.