House in the swamp in chapter 1, where is the key?

If you cross the river using the broken bridge you get to a swamp with one single house. There are some bandits waiting before the house. The door is locked, if you open it you get the message "key needed" which indicates that the door can be opened if you get the correct key.

I have already played through chapter 1 once, but I never found the key to this house. Is it part of some specific quest or is that a dead end that was never implemented in the final game?

You get the key during the troll quest, which is available as a DLC. If you have it, you can start the quest by selecting it on the town noticeboard.

If you opt to help the troll you can ask the guy with the troll head on his wall where he got it and that will eventually lead you to a fight with some bandits at the grave yard and one of them will have the key. If you kill the troll then you're out of luck.