Do I have to sit here and download every single freakin file?

Firefox says "Firefox doesn't know how to open this address, because one of the following protocols (gogdownloader) isn't associated with any program or is not allowed in this context."

When I try to use the downloader... WTF?

You try it the wrong way. The Donwloadlinks you found under the more button are for the GOG Downloader (https://www.gog.com/downloader). If you want to download the game with your browser just click on the left side of the pop-up on each file (Witcher 3 has 7 parts; 1 exe and 6 bin and the latest patch has 2 parts; 1 exe and 1 bin).
After you have downloaded all double click the exe to install.
Or you can use GOG Galaxy to download and install the game (I wouldn't recommend you this for now because it is still Beta).