What should I do in this situation?

I guess you should try and return it to the giveaway creator and inform them that it's against the rules to create misleading giveaways. You can't mark the game as received because you never received the game that was offered, and if you do mark it received without having it in your library it will put you in a potentially bad spot.

Whatever you do, don't mark it as received unless the creator gives you the base game.

check the steam link of the giveaway. if you're sure the giveaway is for the collection, return it and mark it as not received after a week. HOWEVER if it's for the upgrade, then ask the giveaway creator to reroll. i know you can't enter for the dlc for the games you don't own but there is a problem with that dlc. source: my own giveaway.

trips
9XEF0-A7MYK-ZYQZJ

What you should do:

1) Contact the giveaway creator and tell him or her that you have not received the game specified in the giveaway.
2) Wait seven days for the creator to solve the problem (i.e. get you your game).
3) If you have not received the game by the deadline, check the "not received" box, then report the giveaway to the Mods as "wrong game."

What you may choose to do:

1) You may keep any other games the creator chooses to send you, or you may give them back. If he/she asks for them back, I'd do that.
2) If you decide to keep the "other games," and the creator does not ask for them back, you may do whatever you want with them.
3) If the giveaway creator wants to solve the problem but needs more time, you may give him or her more time to "make it right."

Okay so I did contact them, but there was a language barrier because they didn't speak English (my first and only language)... What they basically told me (from what I could understand) was a thanks for joining the giveaway and then to mark the giveaway as received, and to just use what I got however I wanted since I couldn't use it. That's all I heard from them.

The giveaway page specifically says "Trine 2 Collector's Edition", so I did receive the wrong thing (or at least an incomplete form of the thing I was supposed to get).

I'm going to mark as not received. Maybe then the giveaway creator will notice they've sent the wrong thing.