I see there are patches for it, labelled 3.1.1. gog-9 and 3.1.2 gog-10.
What do these labels mean, and is it necessary to apply the patches for the game to work properly?

Thank you. :)

No, it isn't necessary to apply the patches if you just downloaded the latest version of the game which is the 3.1.2. It would be necessary though, if you had an earlier version of the game and wouldn't want to re-download the whole game. As for the labels, it's quite simple: the 3.1.2 is the version of the game while the (GOG-x) is the version of the GOG installer. GOG may update it's installers and thus the (GOG-x) will advance by one number, but it isn't necessary for this to be done simultaneously with a new game version.

TL;DR If you have downloaded the 3.1.2 version (which is two parts in your library), then you don't need the patches. Also, if you're curious, just download the patches, try to install them and you'll see that you won't be able to because you already have the latest version of the game installed. ;)

Again, thank you for the more detailed explanation. :) I just bought the game today.

You're welcome! :) HK is a great game; i hope you didn't miss Dragonfall and Returns too, even though the latter got some criticism for being too simple, especially when compared to the sequels; i enjoyed them all to be honest. Cheers!

I have Returns and Dragonfall too.