However, the clip reveals that they're still using a long-duration laser shining instead of a high-powered short-pulse concept (the power in kW doesn't say anything about that - it's the energy that's decisive).Impressive clip. It's not clear how long the laser took to disable the target.
In the clip it's rather clear that the laser takes a while to melt through the outer hull of the UAV, creating a hole through which ignited fuel then escapes; this is congruent with the UAV keeping up flight, then losing stability and finally going down. With a short-pulse system, we'd instead see a small explosion ("phase explosion") in the impact area before that flame erupts.
Just for comparison, a Phalanx at intercept range imparts about a hundred times as much energy on the target as this laser over the same period in time. Then again a burst over this much time would be overkill from a Phalanx anyway