Yes, that's the same cast-on. It looks different, because she doesn't bend her left thumb, so the yarn appears more twisted as she's pulling the loop through.
I've actually found the Norwegian Cast On to be very tight and innelastic! But now that you're both saying you've read that it's elastic, I'm wondering if it's because of the fact that I really have to tighten it as I work it, in order to keep the cast-on even. Because the yarn is so twisted on itself in this stitch, it doesn't glid naturally into a consistent knot, it has to be yanked and pulled into place, and because of this it's hard to keep it even, unless you yank and pull it to the point where it won't tighten any more! At least, that's my own approach. I'm not super happy with the results though. If you find any tricks to working this cast on, let me know!
In my own experience, the standard long-tail cast-on is the stretchiest cast-on around. I'm very curious if it's possible to work the Old Norwegian so it's actually stretchier than long tail!