I am no lawyer. Specially not American Lawyer.
But I know American definition of solving puzzle and winning lottery. Found out gambling with Americans. :-) They mean human effort and skill to solution.
Competition among people, with clues and people work from clues to answers, is "puzzle", or "game of skill."
No clues has Bitcoin mining. Just guess, guess, guess. No skill involved; only speed. Also, not human effort. Without you can computer win or lose. You not can make computer win more. Nothing you do can help. American law says more like "Lottery" is this.
Not sure "lottery or puzzle" right question is though. Lottery run many times, possible positive return, not chance to lose money, is, maybe, funny random payment schedule for work. Winning computer closes block, produces something others value.
Produced bitcoins dilute bitcoin same others hold. Could argue, maybe, paying you for service are they. Seems fair. But not something gambling with Americans taught me. About this just guessing.