When I tried to install this update it kept saying that the build is undefined.
Either uninstall the game and reinstall this exact update, or download the file outside of itch and open the file there. I believe it's something with Itch.io itself but outside of that the build works.
Does it save my progress?
Yes It should save your progress if you uninstall and reinstall it from Itch.io or if you download it and unpack it outside of Itch.
Edit: I Should mention that If you still have it installed on itch and download and unzip it outside of itch it should still have your progress saved.