No game should save gigabytes. Even megabytes can be too much. If the game is very linear a save could mean a single number. Even if it has character cosmetic customization and a convoluted plot with lots of choices it’s still usually in the kilobyte range. The larger saves (overall) would be sports games like rally racing where the game needs to be able to provide a thorough replay of every race.
system state is not the same as a save file. System state is the cpu registers, the process’ entire memory space (because you don’t know what the game might do at any point) gpu context, etc.
edit: example: the save file for older games was measured in bytes. System state is much larger han that. It contains everything not just what the developer decided to allow you to save.
