An example is the 'Tower of Hanoi' game: https://www.wikiwand.com/en/Tower_of_Hanoi
Another example is this sorting game: https://imgur.com/a/NrjSHdG
I am interested in teaching some very young people these concepts, in a fun way, without the requirement of a computer or any electronics at all.
There are many algorithms which can be demonstrated with playing cards, but they are not games or toys in themselves, but demonstrations.
Based on the imgur link (which finally loaded), my suggestions are probably not age appropriate.
Wood Gears [1] has some neat contraptions and ideas that may be enjoyable for kids (some more than others). Even things like the solitaire puzzles are algorithim toys [2]. There are many variations of it which scale down to be more appropriate to younger children.
[0] https://boardgamegeek.com/boardgame/18/roborally
They have a few specific toys they work with, but it also will likely give you more ideas.
There's also a 1-dimensional version you can play in a classroom with people or on a table w/ coins or chess pieces: https://www.youtube.com/watch?v=KizRWfuT5uQ