Well, we definitely recommend that you do use the itch.io client because that way you'll automatically get the updates whenever we release them.
In theory you could download the ZIP from the website and extract it over the top of your current game - but a much, much better way would be to go to where you currently have the game, go into AvenColony\Saved and move your SaveGames folder somewhere safe. Now delete everything, extract the ZIP, put the SaveGames folder back in the Saved folder (you may have to create it!) and then you'll have a fresh, clean install.