not really, it's not that simple. In its core every game makes you repeat the same thing over and over without expanding much on gameplay mechanics if at all, people play roguelitelikeish games every day and don't have problem even with that.
It's like you are saying that only the very first game of chess is fun because later it's the same game, rules and mechanics don't change.
Puzzle gaming often is about addictiveness (not unlike arcade games), for example let's take Letter Quest, according to your definition it is a filler the game, because you just make words of letters all game long and there are no any other mechanics present (there are upgrades, but that's an RPG part, not puzzle part) and it is a long game. So why do we play it? Because we like the process. If you don't like the process, no additional rules or mechanics will change that in any significant way. It's true for most puzzle games. That's why I like LYNE so much, because I like process and calming, zen effect, not because it is OMG awesome puzzle game. Even Hexcells you name as example how puzzle games should be made have a lot of filler and introduces only couple of new things during all those levels.
you misunderstand me
like i said, it doesn't have to have a new mechanic or rule to be considered "not filler", but it has to have either a forward (new mechanics) or lateral (new use of those mechanics) shift that reveals new sides of itself for it not to be a timewaster. it doesn't have to be fundamentally different, but it has to be different
enough , it can't be a slightly different version of the same puzzle, it needs to make you appreciate the mechanics from a different angle for it to be really "meaningful".
it's kind of hard to understand and i prolly do a bad job of explaining it, but i'll give u an example with hexcells infinite. if u played it u know the game has that randomized mode that just makes a random level for you. now i dunno if you played many of those, but i've done like the 40 you need for the achievement, and playing every single of those levels, even if they used different mechanics from the game and different layouts it was kind of always the same process in my head to solve them. there were no eureka moments or things that make you go wow or have a better understanding of the game, they were all the same puzzle with a different hat.
now the real game levels, there's just a few of them and like u say they mostly just use the same mechanics as the levels before them, but because they're hand crafted and designed around you figuring them out in a certain way they're much more enjoyable and rewarding to go through. i think there's somethign to be said about hexcells 2 and 3 being kind of filler since i don't think i got as much from them as i did from hexcells 1, but just the main levels from any of those games on their own all feel like you're learning more about the game and getting better at it, not just grinding out the same thing over and over
using your example of chess, the thing about chess is that the board and pieces is the same every time but the players are different and the depth of its mechanics is so insane that no two games are the same. and while the pieces behave the same every game, the players use them in ways that reveals new things about the game mechanics and that's why the game is so insanely well designed. same with go, or even tetris, which does something similar with randomization and just how much mastery you can achieve in that game. the rules might be the same but the experience is different every time because you learn a little bit more about playing the game
and randomization or multiplayer isn't just the be all of that, the game needs to have enough depth to feed off those. something like tic tac toe is multiplayer but you try it a few times and that's it, there's a solution to that game that ends there and that's it. and there are games that use randomization in ways that don't necessarily show off anything new, you can play a billion games of solitaire but every game is kind of the same
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so like, it's fine to like games that repeat themselves over and over, but i think there are better uses for ur time than that. just like crossing off markers off witcher 3, i feel like insane level counts on puzzle games are pretty much turning our brains off and just going through the motions, and it's really easy to fall into that trap and i kind of really dislike that.
edit: "adictiveness" as you put it is not something i want out of videogames and i really hate it when i fall into that with open world games like saints row and witcha. personally i don't find anything valuable in that and just feel like videogames are just really good at working your brain towards just playing a little more for very little reward and that's not something im comfortable with