On Windows you have to select the "Windows.zip" Version and not the Game Jam Version. The Game Jam Version doesn't save the game and i think it is Older? I'am not sure, some Features don't exsits i think.
The Itch-App will Install the Game Jam Version when you click on Download, you have to select the Windows.zip-Version and not the Download-Button.
On browser i't will save your game too.
I don't Use Mac, but i think you also should download the Mac.zip and not the Game Jam Version if you are on Mac
(Sorry for my English)