Yes, you're right.
Had a look at some close up photos from a second hand unit available on E-Bay, and it does look as if the motor drives tangentially to the steering column, possible with a worm and wheel type engagement thus increasing the turning effect of the steering column itself, rather than on the rack.
Interesting to know how the system senses the input torque from the driver on the steering column, and presumably it's speed sensitive so that there is little help at high speed and a lot of help at low speed.
Is there a separate control unit on the Jazz power steering (as there is on the Honda in the video) do you know?
I really like that bloke's videos - fast and well informed - watched one where he took a scrap Subaru boxer engine apart and described it as he went - same tooth brush and and universal spanner (aka disc cutter