At a certain time you can see the rocket at two places at the same time.
What you are seeing has nothing to do with compression artifacts, but is frame-blending due to the slow motion effect applied (in the video)
Let's say the video is recorded at 30 frames per second. You only have 30 'pictures' per second to capture the information. If you want to slow the video down (to be able to see the rocket more slowly) you could play these frames back at a lower speed, let's say 15fps. Each frame will be visible twice as long as when playing back at 30fps. (you could also duplicate all the frames, and play them back at 30fps to have the same effect). The footage will kind of look jittery when doing this, like it is stuttering to continue, which is not nice.
Instead of just adding copies of the already existing frames, extra frames are calculated in between. The easiest way is to just calculate the average between the frame before and the frame after. This way all your frames will have different visual content and it will be a little more pleasant to the eye. The fact that you are seeing two rockets, is due to this averaging.
There are other possibilities to generate new frames. Software like twixtor does some advanced calculations and will (try to) guess the rockets position on the frames in between. If configured correctly this is even more pleasant for the eye than the averaging method.
The obvious solution would be to shoot these kind of shots with a high framerate. If you shoot video at, let's say 1000 fps, you can slow it down to 30fps (33 times slower) without having to calculate values from in-between frames.
These artifacts are probably coming from the original video itself, because if you watch closely you can also see it at the original speed. But it's always possible that youtube also uses averaging for it's slowdown feature, so that these artifacts are introduced by the player.