Why? Well we don't usually build our machines and other artificial physical systems to exhibit chaos. You wouldn't want your car engine to be chaotic, now would you?
If the initial conditions were changed just a tiny amount, you would also see a complex dynamical evolution, but a very different one.
So the double pendulum exhibits chaos---but NOT KAOS.
As a result the motion is perpetual motion which is impossible in reality in the macroscopic world since one can never absolutely turn off all dissipation. One can make it very small in some cases. So the animation represents, an ideal limit that can only be approached, but NOT reached, in the macroscopic world.
The microscopic world? That takes a bit of a discussion will NOT give here.
The animation repeats after awhile as one can see. So you do NOT see perpetual motion even though it does exist for this ideal system.