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Uninstall/Delete the old version, then install/unpack the new version.
Itchio app doesn't even do that, it just packs the old version into a new folder inside the new installation. So you have to manually go find the folder and delete it yourself.
The save files and config stuff are in a different place, so doesn't matter what happens to the installed folder, but yeah overwriting not advised, considering you might just start gathering deprecated files.

If you're using Itchio, select the game, gear icon, manage, and choose update if it has one, or check update.

edit:
Nice after the 0.87.8 hotfix, now it won't create duplicate folders or double the game folder size, will just download and update what's needed.