Klaus lets her go, because there's nothing else he can do. If she can't see how she matters so much more than Elena, if she expects to be given everything straight away... He's offered her enough, more than he's offered anyone in a very long time, and she's kept turning him down and using his affection against him and his family, until they got trapped here, and suddenly it's not enough for her. So yes, he lets her go, although he does whisper, right before the door slides shut behind her, "I'll see you around, love," like it's a promise or maybe a threat or both rolled into one.

It might take years, but she'll come back to him at some point, whether they're still here or in their world. He knows it.