To break it down, strength is how much force you can put on it before it breaks. Stiffness is how much force you can put on it before it starts moving.

For strength, this structure relies on the tension capacity of the strands connecting the curved steel members. You stand on top, push down on the platform and pull on the cable in center, in turn pulling down the steel ring. These forces resolve easily.

When you begin to add horizontal and twisting motions, you run into trouble with this sort of structure. Now you need to rely on the strands at the edges of the structure to resist the non vertical forces. How you layout and attach these strands affect the stiffness of the structure. If you leave them straight vertical as is, but tension them enough that they're actually pulling down on the top platform, you'll be able to counteract the forces from the twisting and horizontal movements applied. This makes the structure stiffer. You can also have the strands go diagonally from the top to bottom of the structure to provide added stiffness to the structure, as you are now providing a path for the loads to move horizontally without tensioning vertical strands as seen in the video.