Yes, but the blocks in that puzzle aren't falling from the top of the screen at an increasing rate of speed. The Layton block puzzle lets you take your time and think to solve it. Tetris type games are nothing like that. To me a puzzle is something you can take your time and think about to solve.
Genre definitions are a broken system. It's a similar argument to the one around hack & slash / beat 'em up / character action sharing a similar basis in the 'action' genre but having various defining features and other semantics that make little sense when framed against their genre's definition in a literal way.
Think of it like this- each turn in Tetris (a.k.a. each time a new piece appears at the top) is a miniature puzzle in and of itself: you're being tasked with placing it in the most optimal location based on its shape and the existing configuration of blocks at the bottom of the well. Time is a factor, but the core gameplay loop the player executes boils down to 'solve for x' over and over again with the fail state being "solve wrong enough times to fill the well", versus "fail to solve it at all" for something more laid back like Layton.
Heck, if you want to go all the way with the literal definition of 'puzzle' - "to offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve
: challenge mentally" - then you can apply it to almost any skill-based videogame, because videogames are fundamentally about being presented with a problem and having to solve it. Take Street Fighter for example- Ryu just threw a hadoken at me, do I jump forward/neutral/back, do i block, or do I power through it with a special move of my own? The 'correct solve' in that case would be whichever one means I don't take a hit.
