My guess is that they’ve used some effects in photoshop to make still pictures of each character or item and then animated it in something like after effects.
There are some plugins that can turn a picture into that style of drawing, such as Andromeda Cutline. There’s Akvis Sketch or redfield Sletch Master for a basic pencil sketch effect. You can also use blend modes and coupled with patterns and other effects to build up your picture into something similar. You can also use Illustrator to create some of the cut line effects.
Looking closer at the animation, there’s only a few individual bits that make it up – the wale, the tenticals, the octopus, the globe, the ship and not much more. If I were to try and reproduce this, I’d be quicker to just draw it all by hand on paper, scan the images, cut them up and polish them in Photoshop and then animate the bits in After Effects.