If you look at the headstock end with the pulley and runner removed, you see a sort of V block in there. There are jack screws at each end, with holes around their head permitting a rod to be used to turn them. Tightening them pushes the block upwards, loosening (and then inserting the runner and firmly tightening its lock screw) pushes it down. The V block is slit along its length allowing it to flex, thus being able to move up or down in the round bore. This is for the vertical alignment. Then, a simple tool can be inserted to rotate that block in the bore, which gives the lateral adjustment. Some tools have a more obvious vertical adjustment (see pic), those dispose of the jack screws but the lateral alignment can still be done.
To check the alignment I just use a wheel with the shortest possible pivot to pivot length, and put it in the tool (check that the wheel is true!), and see how it looks compared to the tailstock runner face. The short arbor magnifies any error, and if it "looks" good in the tool, that's good enough.
One thing I have seen on many of these is the simple headstock runner is bent. To check that I put it in collet in the lathe, and check. I use a dial test indicator, but again, if it looks like it turns true just visually checking against the T rest or something, that's probably good enough. Truing it is simply a matter of bending it the right direction. I haven't broken one yet.
As to why Steiner moved to this design- I imagine it makes it easier to produce, as things are less dependent on getting the hole for the headstock runner absolutely perfectly placed. And it just nice to be able to adjust things if and when needed.