What telescope is this, and how does it work?
This is indeed the VLT, or rather one of the four 8.2m Unit Telescopes (UT in ESO parlance). Looking at the optical layout (found here along with a description of the telescope), the small mirror in the centre of your screenshot is M3, the tertiary mirror. M1 is the primary (in the background), and M2 is out of the frame towards the top- the white supports you see in the foreground hold it above M1.

One advantage of this design is that you can have two large instrument platforms on the vertical tilt axis of the telescope - this way, you don't have to dangle several tons of instrument from the support structure (Nasmyth focus in the image).