Yes, it's functional. It's mounted to the engine lid, which has been reinforced, and ties into the forward cargo bulkhead with a hood pin. It does not have an overly extreme angle of attack, it likely appears so to some as the rear of the car is significantly lifted on the dyno. Also, it's not an Exige wing, it's a custom carbon piece that's no longer manufactured.
The car was originally the hypersport prototype turbo car, which I put a good deal of work into in an effort to make it about the craziest Elise on the street, and certainly the best one available to rent.
The diffuser is slightly higher as it's on a redesigned upper mount, though it looks considerably more so as it's on the rollers in the video-- the rear clam is removable (4 pins, about five minutes).
As for why put that kind of work into a rental car-- well, that's what we do. All of the cars are modified to be the best of the best, and kept in pristine condition, as they're marketed to people who want the best possible experience, and not a car with pieces hanging off and discarded CDs rattling around under the passenger seat.