Arcade games or handheld or video games didn’t have any storage. Even on old home computers if you’d want to program in a save feature, you’d need to instruct the user to change to a fresh cassette for save. Then back to the game tape for reloading the game. And rewind and find the save on top of that to load.
It took a long time before floppies became ubiquitous, even longer for hard disks.