Unrelated to the game itself, sorry. The description says that "If on ... Linux, simply delete the old game folder and download the new build. Your saves are stored in your local files, so they should be retained after the update." Now I don't know how it is Windows or Mac but on Linux the game saves are saved within the game folder, in ./game/saves. In order to update on Linux you should just install the new version and manually transfer the save files over and then delete the old version if you so desire.
AFAIK. Renpy should have both local and global (central) save folders on all platforms.
Local being in the game directory and the global directory should have save folders of every single game (on Windows AppData\Roaming\RenPy).
On Linux the global directory should be ~/.renpy/game_directory.
BTW. If you ever want to nuke saves for a game, you need to delete both the local and global save folders for that game.