The writers who created the fictional character, Captain Kirk, and had him apparently extemporaneously invent a game with complicated rules called "Fizzbin" cannot be considered an unintelligent source for the aforementioned information content. In every case where the origin coded information is known, it is the product of a mind.
You said that intelligence from non-intelligence is not as mysterious (as life from non-life) But there is no naturalistic, physical/chemical process known to science that creates coded information. The examples of animal intelligence that you listed are derivative of the coded information programmed into the animals DNA, which begs the question of the source of the original coded information in the DNA in those animals.
Cordially,
I said what I intended on the subject in the five paragraphs following the pull-quote about "intelligence from non-intelligence is not as mysterious". I'll add this: Many remarkable abilities developed spontaneously in the long chaotic time following the Cambrian Explosion. Flight would be one of the more interesting ones. Why not intelligence?
That I do not adhere and respond to your challenge to explain rigorously how information theory, or any other, applies to my casual suggestion need not be taken as a surrender to your mastery of understanding on the subject, but more perhaps to its irrelevance to the discussion.
Animals involved in the day-to-day challenges of survival and procreation did not have time to formulate complex understandings of the underlying principles involved in the remarkable things they were doing. They simply did them, whether they were impossible or not.
"But there is no naturalistic, physical/chemical process known to science that creates coded information."
However, The functioning of genetic material during mitosis, meiosis, and reproduction in general is such a process. It involves the functioning of imperfect reproduction, along with a selection process, and the introduction of various means of modification of the subject matter. Under this scenario, coded information cannot help but change, and necessarily also grow in size.
Such a process may not explain the origin of this kind of information, but it does explain its growth and continuing "creation".