For windows and Mac, the save game files are always saved outside of the game itself (somewhere under your profile in windows, somewhere in your personal library in Mac, google it if you want to know the exact location) so you can overwrite the whole game, and it will still find the save games.
However! The dev said the saved games are not always compatible with this release due to code changes so you might have to replay everything or use the Episode Skipper he added to the game.
Viewing post in [0.8.0] Public Release! comments
First off, are you playing on windows or Mac or android? That might help.
Secondly: yes, that's it.
For windows or Mac (I don't know about android), you download the zip, unzip it where you want it, and play. If the saved games are compatible (usually but not always) you can then load the latest save (it'll find it) and continue. If you get an error (screen with text on it), then you can try to restart the game and load an older save - sometimes that works.
The saved games working or not working depends on how good the person programming the game planned his or her game. It contains the state of all the variables in the game, and if the dev suddenly realizes that he needs to add a new variable to keep track of something important, the saved games are usually borked and you need to restart playing the game from the beginning.
In that case, as explained by the author: you don't load a saved game, you just select the last episode you played and start from there.