I think big mountain riders work out properly more often than freeskiers. Problems in this video:
1) Standing on swiss balls does nothing other than risk ankle/knee injuries
2) You can get "cardio" better ways than in a gym on equipment (sprint repeats, hill repeats, trail running, bike sprints, CrossFit etc)
3) He is doing hip extensions wrong on the swiss ball, better to do them on the GHD type bench so you can get a full range of motion from the hips (he is trying to strength erector spinnae in lower back)
4) Yes being flexible is key to preventing injury, but you have to be strong through the range of motion too (e.g. weightlifting) if you want to be safe from injury in a position with load on the body (landing a jump)
5) Number one issue really, you need to do heavy squats with good form. Period. Low reps heavy weight is how you will build total body strength not just legs. 5 reps for 3 or 5 sets is the way to go, progressive loading etc. My prediction is that unless Jon gets his squat up a lot, to at least 1.5X-2X bodyweight (so 120-160kg) , he will not be competitive on the world cup/olympics in GS.
All the said he is a crazy good skier, if he just tweaked some stuff he would be even stronger and it might help him a bit more who knows.