As I understand it, the one in the link is a very, very fine commercial model. The artillery Luger would have had a slightly different sighting system, and either a simplified shoulder stock (Navy), or the holster/ stock combo, and of course chambered in 9mm Para (this one was not).
This one in the video is something that a competitive shooter or designated "Fancy Person" would have owned.
Not a military workhorse, but the best a Luger can be (except that it's in 7.65 and not 9mm).
