I'd call DE:HR or Thief more player driven, like the Witcher 2, but they're not fully open world. Yes, they both offer small sandbox areas, but ultimately the game still locks you into events and cuts out parts of the game when it wants the story to move forward. A big determining factor to whether a game is open world is if it cuts out areas you've already cleared, or leaves them open to revisit for no reason.
Games like Dark Souls or Overlord: Raising Hell fall right on the edge of this, but since they only get bigger as the game progresses and don't close off any past areas, I'd say they fall on the open world side.
Ofc, 'full' open world games include titles like Skyrim, Minecraft, or Sacred 2.
People tend to think full open world is better, but I'm not sure I agree. There are positive sides to the balance of freedom and focus that games like DE:HR or Dark Souls provide. They balance open gameplay with linearity, ensuring detail and unique content remains amazing, without railroading them down a tiny path or sacrificing exploration. If you look at Skyrim (not one of my favorite games) most of the content is copy-pasted dozens of times, if not hundreds. If you look at Dark Souls, for example, it keeps most of the sense of exploration but with a much higher density of unique content. That's why semi-open, semi-linear games like DE:HR, Dark Souls, Dishonored, or Dragon Age Origins feel more like a real adventure to me than games like Skyrim; you can still mostly go where you want, but without running through the same copy-pasted ruin 10000 times.
Some people call open world games more realistic... Also, not really true. There's nothing realistic about walking through a town made of the same 3 people copied over and over again with slightly different faces (sorry, picking on Skyrim again). I much prefer the system used in Demon's Souls/Dark Souls/Dark Souls 2, where in each game there are probably only ~15 NPCs, but they move about the open landscape, all uniquely voiced and uniquely written, adventuring or settling based on their own goals, personalities, and histories.
And when characters die in Dark Souls (if they die), they're dead. No getting them back, no reloading a save, sorry, you just lost the only high-level blacksmith in the game. That's realism. Not seeing "Jarl Balgruuf is Unconscious" on your screen and knowing that any second the psychic respawning guards will teleport through the doors to attempt an arrest (unless you hit f12 to undo the last 5 minutes).
Weeeeell... I guess I sort of turned that into a list of ways I think Dark Souls is better than Skyrim, rather than just an answer to what constitutes an open world game. o_o