If I downloaded the 19.09.20 files (the one for Windows) and start fresh/new game, I don't need to download the update files (the one that 20MB), right?

Correct. The update files are for when you have the previous game version and want to update, in this case from version 19.08.24 to the new version 19.09.20. The full game always has all files, so it's not necessary to update them after the download. :)