Correct if I'm wrong, as I don't know much about "Touge" races.
Having a race on a public road does not require a street legal car.
If the race is a) officially sanctioned then any car could be used, or b) illegal street racing, then again, really any car can be used as you're doing something illegal anyway.
We have a hillclimb event every summer on a local, public road. Plently of non-street legal cars compete in the race. They are trailered to and from the course.
That said, that car may well be street legal, I don't know anything about it.
And in general:
All street legal means is that it complies with the local and national regulations. These include ride height requirements, headlights, taillights, reflectors, the kinds of tires, brakes, emissions, etc.
For an amusing comparison, there are plenty of raised trucks around here which are
not legal, however a McLaren F1 is 100% legal to drive on a public road.