@Rodread provided me a very interesting video containing the power curves I was waiting. I put below a similar but shorter video which contains useful data. It is a big file so opening it takes a long time. Opening it in a new tab makes reading easier.
For what I understand the beginning of the video shows the take-off phase, then the kite in operation from 16:00. The wind speed aloft (first circle in the left) was about 8-10 m/s. The kite speed was between about 38 and 56 m/s. The power generation was negative about half of the time (kite slowdowning), and between 0 and -500 kW, the positive power generation (kite accelerating) having the same values. So there was roughly no generation in average.
An older video (below) represents Wing4e Energy Kite Prototype. It produced between 4 and 8 kW (wind speed about 10-11 m/s). Small flygen AWES seem to work better, undergoing a lesser weight penalty.