Having never used a sewing machine, I would imagine they you pull the leather taught along with a certain amount of stretch to the elastic, and sew. How did they make them in the first place, I wouldn’t know of course.
Now I'm curious too. I often just like to imagine how I'd go about fixing something and it usually turns out I wasn't as far off as I thought I would be but here, I'm lost.
I know that on German jackets, they use a strip of stretched elastic tape, stitched to the part of the leather that is to be elasticized. Lol!