Casey, I wouldn't go so far as to call what Oxer's trainer is doing "rolkur." Yes, Indy is behind the vertical, but rolkur (or at least my understanding of it) is more drastically behind the vertical as well as lifting the horse's head and neck up to create a dramatic curve to the neck/poll.
To me, it looks like the trainer's hands aren't as quiet as they should be in the sitting trot and Indy is getting behind the vertical so that she isn't bumping him in the mouth so much. Honestly, I'm not entirely sure what's going on with the trainer's hands in the first part. She's got them really wide and her wrists are kind of curled under so the top part of her hand is facing forward. That's shortening the reins quite a bit, so that, combined with the "all-over-the-place" hands is making Indy go behind the vertical to avoid the pressure and bumping. Indy's mouth isn't gaping, as you'd expect to see with a horse forced into rolkur, so it doesn't appear he's having extreme difficulty breathing or is desperate to avoid the pressure.
Oxer, Indy is very cute. I love his trot. It's adorable. His jump looks nice and honest, too.