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.
You think that pushing a button that generates a purely random outcome is a game?
To me, those are neither games nor puzzles.
There is nothing one can do, in terms of thought or execution, to influence the outcome.
Other than I suppose choosing to play or not play.
To me, a game must include some capacity of the player to influence whether they succeed or fail, within the game itself.