I could be wrong, but I'm pretty sure that is an exposed elevator core. You can see the two storey extension to the rear built around the 1940s, the elevator would be the only way to access it.
I like this building, known as the "People's Palace" but its never really blown me away. Its a bit too over the top Federation style for me. Not to mention its reputation as the place for sleazy guys to pick up easy backpackers ... THe Bellevue was a much more elegant precedent.
Here's an old photo from the State Library of QUeensland without the intrusive extensions and the ugly towers surrounding it.
THe post probably belongs in Beyond Victoria anyway.