The engine has higher compression ratios than cars that use "regular", and also derives its power through a more advanced ignition timing. The higher the octane rating, the more the engine can advance timing. Running lower octane gas in your Mini will lower both your power output and gas mileage, enough that it will…
The whole thing is just a gimmick.
I asked a buddy of mine if he could imagine his 17 year old racing in F1. This was his response: