Indeed (from take-off to operation phases), the boom (and the drums) seems to point more and more perpendicular to the tethers going to the kite, excepted during take-off where boom and kite are aligned (before tether unwinding).
Do you think this would then be a lever type conversion system, with the drums only being used to unwind the necessary tether length?
In my opinion this would be surprising, because it would mean that the generator is driven by the rotation of the boom, which seems unlikely to me.
It seems to me that during the take-off phase the boom (and therefore the drums) points directly towards the kite, as shown in the beginning of the video. We then see the shift between the orientation of the boom and the position of the kite as the tethers unwind in order to start the reeling cycle. In my provisional opinion, it is the continuation of the take-off phase, using the dynamics of the boom as you suggest. Otherwise, of what use would a boom of around twenty meters be compared to the hundreds of meters of tether in operation?