I don't do sudoku, so I cannot comment on that, but I have some experience with both chess and crosswords.

The thing about chess is that players have to think through the potential consequences of their moves if they are to win, so it teaches players to identify threats, assess the level of risk from each threat, and identify the least costly action to counter each threat. These are critical life skills, but playing chess is educational only if players also learn to transfer the skill from the context of chess to the rest of their lives. Clearly, the world of chess is full of twots who never learned to do that (we're looking at you, Bobby Fischer).

A good crossword puzzle forces solvers to ransack their mental trove of trivia for details they might never otherwise bother to retain, let alone recall; for example, everything I know about major-league baseball, golf, and all forms of American collegiate sport was learned in order to solve the New York Times crossword puzzle. Other people might be driven to Google for the names of television actors, Second World War generals, or types of igneous rock. The puzzle itself has little value, but its random nature takes the solver into territory that might otherwise never be explored. I believe that is a Good Thing.