When the rocket speeds by we see its length has become shorter than it was at standstill.

Length contraction makes rocket slices thinner than they were when the rocket was at rest relative to the earth. We see the past and future of the rocket compressed in the direction of motion. The compression rate is the same over the whole length of the rocket and doesn't change in time as long as the speed of the rocket doesn't change. It worsens with higher velocity, just like timedilation and timedissynchronisation.

In fact the rocket doesn't really shorten. You see the front of the rocket on a moment in the past when the rocket hadn't progressed that far yet. And you see the rear at a moment the rocket has already progressed further than it has in the now - your earthly now. And because front and rear are nearer to each other the rocket between them must have been shortened.

The rocket captain on board sees his own ship normal as usual. It is not shortened. The shortening in the picture aside must have had a different cause.