What makes GoL in GoL somewhat magical feeling is less "there are layers of logic being executed" and more "GoL rules and conditions are extremely restrictive yet still just complex enough to simulate nested execution of the ruleset itself". When you move up the complexity chain to "person with a sheet of paper" you lose some of that wonder to just end up with "extremely complex system can throw away most of the complexity to also simulate execution of a simple system" which feels a lot less surprising.