Sophistocated stuff but I imagine the soldier had enough stuff to drag around. And how do you get an enemy soldier to come out and stand up straight with nothing blocking your view.
Well, since those range finders are about the size of a playing card and were a standard issue with the Berdans, they really weren't a lot to lug around. Plus I would imagine that people got kind of good at estimating range, and coming up with work arounds (ok, he is kneeling, so he is about half as tall, card says 350 yards, soooo...yeah, sights set to 700, aim for the belt buckle).
But, more than likely it was mostly done by eye. You knew that certain things could be seen at certain ranges. The famous "Dont fire until you see the whites of their eyes" was a kind of standard order. You can see the whites of eyes at about 20 yards. You can see the eyes as points at about 100 yards (I think I have that right). With a bit of practice, you can come pretty close in your estimates. Good enough to adjust your sights and get hits.
I've played with reproductions and checked what they say against a laser rangefinder, and they were pretty close. At what the laser said was about 830 yards, I got about 850 with a stadia. Again, plenty close enough.