Surely the chain should be as close to (or as you say, below) the centre of the pivot point as possible? What else am I missing?
The Streetmachine has the chain slightly (how lightly depends on selected gear and suspension loading, but a couple of centimetres) above the pivot, and IIRC the Grasshopper is similar. As that 1" steerer shows, it's an old design by today's standards. (I kind of get the impression that HPVelotechnik are tired of the Streetmachine, but it remains popular because it's such a good bike for fully-loaded touring.)
One thing I do like about the Streetmachine geometry is the extremely straight drive-side chainline. Depending on boom extension and gearing, the idler practically disengages in some combinations (which is presumably why they don't use a toothed idler). IIRC the idler does a bit more work on the Grasshopper, and certainly the Speedmachine.
The ICE suspension allows the chain to move freely beside the pivot, but with derailleur gears the exact position is quite sensitive to which gear is selected, it being worst in the lowest gear, where efficiency matters most. It's spot-on in the middle of the cassette, which is about the same as you'd get with a gear hub. Of course it's quite a firm elastomer suspension, and I've certainly never thought of the Sprint RS as bouncy while climbing on it (indeed, it could do with a bit more bounce at the front end, but that's another matter).
Nazca seem to have the right idea, with the drive-side idler enforcing a chainline right alongside the centre of the pivot.
*googles*
I hadn't seen that catrike system before (I've only met rigid ones in the flesh), but for these purposes isn't it only the first linkage (which seems to be alongside the chainline) that counts? The rest are just levers acting on the shock unit to move it out of the way and probably do something to the travel.
ETA: Just thought to check, and there appears to be some variation between ICE models. Their newer 26" Adventure FS design has a second drive-side idler keeping the chainline right through the middle of the pivot, Nazca-style.