I read that a shorter crank gives you a faster cadence
a faster cadence (in the same gear), gives you more power, which gives you more speed
thats what it's all about (speed)
I don't think you read all of it. A higher cadence in the same gear
requires more power, it doesn't
give you more power. You have to provide that yourself. Generally, a higher cadence is used in a lower gear for the same power and speed. The video you linked to shows training yourself to use a higher cadence and to develop more power through that training.