Right, I don't know if I'm missing something obvious here, but I bought Shadow Warrior 2 a few years ago and recently found out about the later patches. I thought I'd install the one that added actual content to the game rather than just bugfixes, but when I tried, it told me that the patch does not support this version of the game and prompted me to download a new installer.

The problem is that I don't know what it means by that. Does it mean that I have to redownload the entire game, or is there a specific file that I have to get? If so, where from? The GOG Downloader Links in the library are all dead. I would appreciate some help with this one.

Oh, and I don't have GOG Galaxy. It never seemed necessary to me.

No idea which version you have but I suggest downloading the current installers for the full game. FWH has added much content to the game later like Way of the Wang or the Bounty Hunt DLC.

I have Way of the Wang, I'm not sure how to check version number, and where would I find the current installers?

In your library of course. The current installer version is 1.1.14.0.