I think the argument that chess has improved my underlying hardware sounds reasonable, but it's also necessary that hardware be able to adapt to different scenarios in life. If I spend too much time on chess, it feels like that would end in a place where that hardware would be specifically tailored to just playing chess.
I'm not a chess player, but I recognize that it can be a very valuable tool for understanding what I might call the "while loop" of chess
* any given position has multiple options for action
* how to anticipate what moves an opponent may make in response to each of those options
* how you will, in turn, respond to the opponents responses
IOW, it teaches tactics and strategy, both of which we engage in countless times each day, whether or not we consciously realize it.
I just found at a point getting better meant memorizing a lot of opening game theory, as well as memorizing end game tactics. Then, I'd probably still never be world class because I don't think I'm exceptional at visualizing chess piece movements--I may be better than 99% of all people but the way the top 1% of chess players can do it is just phenomenal. I feel like it's a specific skill that some people just have and get extremely good at. You really need to spend some time playing the game and getting better and better to realize how good at visualizing the ability to think ahead the top players are. Magnus Carlsen never studied chess using a board -- it is just natural for him to think about.
So for a random example: if you can go from comfortably holding 5 random objects in your working memory to 8, that's going to manifest itself in a variety of ways.
I wonder if people get different results from these puzzles based on how they approach the puzzle. Maybe they can solve the puzzle by avoiding the cognitive function the puzzle was designed to use and thus they get no/limited benefit.