Why does the closest approach of star S2 to Sgr A* not appear to be near the focus of its elliptical orbit? Phys.org's Very Large Telescope sees star dance around supermassive black hole, proves Einstein right links to several ESO videos, including The star S2 makes a close approach to the black hole at the centre of the Milky Way.

In the screen shot below, the location of Sgr A* is nowhere near a focus of the elliptical orbit.

In addition to the excellent accepted answer I have written this answer to Why does Earth not appear to be at the focus of TESS' elliptical orbit in this video? and so I know that looks can be deceiving depending on one's perspective.

But I still don't really understand why the offset can look so bad here. For the video did they put the observer (the "camera") at a fairly close distance and thereby distort the perspective, or even if you choose the distance to be infinite can elliptical orbits appear to not have their central body at their focus, or at least along their axis?  

Is it possible to state the orbital elements of S2 in such a way and in some coordinate system so that I can plot them in 3D and then try to reproduce this effect?
The orbital elements are on wikipedia:

$$e=0.884\ a=0.125'',\ i=134^\circ,\, \Omega=228^\circ$$

(At an assumed distance of 8kpc, $0.125'' = 1000au$)

It is the inclination that means that the black hole is not at the focus of the projected ellipse.

Imagine a circular orbit, with a central body.  If viewed from a distant but high inclination, the orbit is projected as an ellipse, with the central body at the centre of the ellipse (not the focus) 

A distant projection of an ellipse is another ellipse, but the projection of the focus is not the focus of the projection.

Below you can see another example.  The ellipse is in the grey plane, with foci at A and B.  But the apparent ellipse has a completely different axis, and the focus is nowhere near the axis.  These image have been generate with geogebra and no perspective has been used.