Possibly a "through the wall" flue as Dave says. Just look outside for any terminal.
More likely, the flue is constructed from gas flue blocks. They're sized to bond in with conventional masonry blocks when laid in the usual manner.
The difference is, they're hollow, with a rectangular hole running through them. In the bedroom, it looks just like a normal block wall. Downstairs, a chimney breast has been constructed to give the look of a regular fireplace.
I'm afraid these are not suitable for wood or multi-fuel. You would need either a full height chimney built outside (or inside), or an insulated stainless steel woodburner flue.