This is very similar to 'owned'.
A way to describe what happens when someone slights you, for example, when they do not return a greeting.
It can also mean when someone gets the better of you. The image is of having a door closed (not slammed) firmly and politely in your face.
- Did you ever get your video game back from Malcom?
- Nah, he closed me.
- Yeah, he is such a closer.