Belated, but the DLC takes the form of some zipped folders, which you just copy and paste into the correct location in your existing installation. So far as I'm aware, it shouldn't matter if you buy / download those folders from itch or GOG.
Late response too, but I ended up buying the game again on steam because it plus the DLC at a discount would be cheaper than getting the DLC here on itch io. Mostly because Steam has regional prices for me, while Itch doesn't.
