I am using the downloaded version
The saves are stored in game, are you saying its not capuring anything at all when you click save? The export option is mostly meant for web based version. Save files for the desktop version do save inside the same folder as the game in the saves folder.
If you hit escape this menu comes up:
Click save:
Select a slot:
Click save in the middle:
This should save your game. icon on the slot changes color to show it has data.