Looking from the outside....it's circuit training with a few added weights, mongo pull ups and a cool tshirt. Any decent boxing/Thai/MMA gym will have circuits as part of their classes. Plus, doing lifts that the likes of Olympians do( except the Olympians will do one lift and walk away) flat out against the clock is going to compromise your form.
I'm sure I'm going to be corrected here but that's my view. Youtube is littered with CF disasters. Basically people working to their expectations instead of their abilities and, more worryingly egged on by dogshit instructors.
On the positive, it's fitness. Just make sure your instructor has a decent base knowledge of fitness and the body and not just done an instructors course and declared himself a Jedi in the art of Cross Fit.
