I've just gotten this game via GOG Connect, because I had it in my Steam Library. I'm planning to play as much games through GOG, but I'm wondering if this is the Director's Cut (which is the version I have in my Steam library).
I assume it is, but I can't find anything about it on the store page or anywhere.

The game's shelf image in your GOG library -- at least, in the web browser version -- even includes the words (hard to read though they may be) "Enhanced Edition Director's Cut". : )

Just wondering why there's a separate item in the "more" menu called director's cut? Do I have to launch that version in the menu to get the director's cut or the regular play button?

see screenshot

That stuff seems to be equivalent to what you could access from the game's Windows Start menu program group; in mine, there's a link called 'The Witcher Enhanced Edition Director's Cut [Safe Mode]'. That's probably all that is. You'll launch the same version of the game either way; I think that link is just if you're having trouble getting the game to run properly when starting it normally. :)

Ah thanks. I couldn't see the [Safe Mode] part on mine for some reason.

I just bought the game today. I was concerned about whether I'd be getting the censored (v1.4) or uncensored (v1.5) version of the game. By default, GOG gave me the option to download v1.5 of The Witcher, which is equivalent to the Director's Cut. Very good to know.