Generally we talk about the cross over functionality of gymnastics being primarily in kinsethetic development. The diversity and rigorous technique in gymnastics sets up an athlete to learn new things very quickly and to a degree that is not matched by many other disciplines. There are a lot of skills that generally transfer over to other activities directly, but most of the acrobatic elements do not necessarily translate directly. The video is an exception.
One thing to note is the ridiculous vertical jump that Jerome has. This would not have been possible without tremendous explosive hip extension. Now, a dive shoulder roll would have actually been more functional in this case, but it is quite impressive in any case. If this had not across the goal line then the front tuck would have been more valuable. A shoulder roll would result in a downed ball, a front tuck would not.
Free runners often add acrobatic elements to their paths, but this does not generally increase efficiency. Performing flips and twists is fun and puts on a good show, but very rarely would it be the right choice if speed and efficiency were the true demands such as in a foot chase. This video is just a good example of where developing an “air sense” can come in handy. Try some gymnastics classes and learn how to keep your awareness in any situation.