That was in my OP though, that most games can be thought of as puzzle games with extra steps.
I just don't get where you're getting "most games" from. If you would have phrased it like "many games can be viewed as puzzle games if you really think about it" you would have maybe had more people agree with you.
I understand your reductive approach - it's just that there are so many games it doesn't apply to that I can never agree with "most games".