Edit: I tried but it said there was an error with the serial number. I double check and I got it right. Don't know why it didn't work.

Edit (again): It worked. It's registered.

The store page has the full game, not patch files. It should have just unpacked a GalCiv2 folder with the whole game in the same location as you downloaded the package at, unless you specified a different place.

You don't update anything. The whole final version of the game is in the package from the store downloads page. I suspect the prompt you got when doing it again was just due to extracting it in the same location as you did the first time.

You can just run the copy you extracted in the location you extracted it, and toss your old copy.

That is correct. We don't provide patch files, just the whole latest version of the game. That is why it was 1.18GB.

You shouldn't need to unzip it again--just make sure you run the copy you unzipped (go to where you unzipped it--any shortcuts you had to run the game will still point at the old copy unless you update those yourself). You can move those files and delete the old ones as you like once you've figured it all out.