When you play tournaments often (or when you play at the go club that two-stones-stronger player you so want to win one day) which means you play very seriously putting a lot of effort to do your best with a generous time setting, and then you review the game just after with a motivated player like you were, It’s not that difficult to remember your moves, at least until late middle game.
To rebuild the game, you try to follow your ideas you had. It’s not an exercise of pure memory (like for a list of names).
The effort to retrieve these ideas you had when playing each move is very valuable and a good preliminary to discuss these with your opponent.
For the very last moves (yose) you have still the stones in front of you to help too.
It’s true that a recording is convenient (which is automatically provided with online play.) but you lose the opportunity of that “retrieving the move” exercise.
The few times i tried was really painful. It took away an important part of my focus, generated sometimes time management problems, was not funny in itself and on top of that i didn’t use these kifus afterward that much!