I am guessing that the HN audience would be / should be interested in that distinction. Mathematically speaking, chaos is an extreme sensitivity to initial conditions, and is very much still in line with deterministic systems. The resulting output, while seemingly random (since there is no easily identifiable pattern), is mathematically and conceptually different from actual randomness.
https://en.wikipedia.org/wiki/Randomness
It really depends on the exact definition of what you are quantifying 'random' to be.
There is no proof (in the mathematical sense) of real randomness.
In this example the path is neither chaotic (in the formal sense) nor random, because a Fourier transform would identify the harmonic components.
The chaotic nature of a system is one thing.
Our lack of knowledge of the governing laws, initial conditions, feasibility of simulation forcing us to use the mathematical tools of probability (i.e. randomness) to describe our uncertainty about said system is another thing.
The reason why it matters is that a statement like "a double inverted pendulum behaves randomly" is just wrong as it would imply that you couldn't even do a simulation of one in theory without throwing some dice.
However, it is totally uncontroversial that if someone gave you a measured initial position and velocity of one with 'really good' precision and asked you to predict its state 5 seconds forward you would likely have a big smeared-out probability density function to deal with.