It's not reductive, it's misrepresentative. A puzzle game is only a puzzle game as long as coming up with the solution is the main task.
There are more than enough games where coming up with the right solution is not difficult, but performing it is.
Also the name puzzle game implies that there are designed puzzles. Any game where you have to make decisions in generated situations aren't puzzle games. For example if you take a specific chess situation and ask which move would lead to check mate in x moves then that's a chess puzzle. That doesn't make the game of chess itself a puzzle.
According to his interpretation of the genre it would be an action-strategy game which arguably fits tetris better. Your underlying point implies that all strategy games are puzzle games which this guy doesn't agree with I think.
Speaking of chess, you might be able to argue that some old RTS games are puzzle games when playing campaign, such as the first Command & Conquer. You often have very limited resources, the AI will do specific things at specific times or with specific triggers, and you're often given specific constraints, like a time limit or keeping a specific thing alive. In this case, though, it's mostly because the AI is so primitive that almost every action is scripted in advance for that specific map.