UPDATE: 5:20 PM EST—
We can now say for certain that the strike depicted happened nowhere near the western part of the country and not at some major military weapons storage area. It happened at a heavily bombarded rural area in the far eastern area of Ukraine.
In satellite imagery The War Zone obtained from Planet Labs, you can clearly see the farm featured in the video. It was partially destroyed by the time the image was taken, on March 12th, 2022, a week before this video was released and news of Kinzhal's use was distributed.
This also answers our question as to the UAV's presence above the target area. The anti-air threat is nothing in Ukraine's east as it is in the west. This also calls into question, even more, why a missile of Kinzhal's nature would be used on a target close to Russian territory and on what appears to be a farm's barn or large chicken coup.
With all this in mind, it is very unlikely we are seeing a Kinzhal missile being used in the video. Whether or not one was used at all, we cannot answer that. Maybe there was another target somewhere, but this was not it.