Engine RPM too high

I assume in the video you are trying to show us that the rpm gauge stays at the same speed? Please verify that this is the case. If so, there is no simple answer, the vehicle must be scanned with a Scantool with BMW/mini capabilities.
Now there is something you can try yourself and it is called a battery reset or capacitor discharge. You must fully disconnect both battery terminals. Cover the bare positive and negative battery posts with a rag. Get a jumper wire and connect the negative and positive terminals (please ensure the terminals are not even close to the battery posts as this can be extremely dangerous if they are even close to being connected).
What this does is it drains all the short term memory from the modules and resets the module. Sometimes it fixes little glitches in the module. I would leave the terminals connected for thirty minutes.