Do you actually have to transfer a game from Steam to collect, or just link the accounts ? If the latter, how do I claim the game ?

Link the accounts, click on the game you'd like to claim, get the game added to your account. It's no transfer, it's an additional copy.

You link the accounts and if you already have this game on Steam it will also be added to your GOG library.

I think perhaps I am misinterpreting something. I was under the impression that if you linked the accounts, GOG would give a free copy of Limbo.

Yes, you are misinterpreting something. The image clearly says "Get LIMBO for free with GOG Connect." GOG Connect is GOG's feature where you can get some of the games, which you already own on Steam into your GOG library. This is, of course, only valid for those games whose publishers approved this. Why in the world would GOG give you free games just for having a Steam account?

Yes, I read through the faq; it does not answer my question.

I have not done this myself, but here are a couple things I've read in other threads concerning Connect:

- set your Steam user profile to Public, so the Connect thingy can look at your Steam library to find a match.
- it's not instantaneous. Takes a few hours for Connect to do its thing but I seem to remember people eventually getting the game added to their gOg library.

Good luck

edit for typo