Really looks like mine. Have someone to hold the metal surrounding in place while you turn the glass dome counter-clock wise for a quarter of a circle. The metal edge is in one piece and screwed to the electrical outlet. I know this post has been online since 2 years, without any answers, although it has 406 views. So I guess 406 persons do have that same fixture. I hope it help to next 406 persons... and surely me in a couple of years when it will time to change the light bulb again and will have forget (again) how to do it...
I've owned a light socket exactly like that one - identical in size to an E27 but totally lacking in internal threads. Mine was simply a manufacturing screwup - the rest of the sockets on the shelf, with the same product number, had the expected internal threads. I got mine all the way home and installed before I noticed the flaw. The store was quite happy to exchange it for a "real" socket that worked.
Replacing that socket with a normal threaded E17 socket is an easy job.
Best Answer
Try twisting the ring around glass part, or twisting the entire thing.
I suspect it's just the glass bit.