Suppose the government made a law saying that you cannot never sell KO (Coca-Cola stock). Today KO is selling for $41.62/sh. Tomorrow, is it worthless? No. It pays a 3.05% dividend, which it typically increases 10% a year. It is worth at least $1.27 (the first year's dividend).
Now to the question about cats selling for $500k. Would a sensible taxing authority or professional auditing firm assess a flower at $500k - $1 million? In 1637 a single Viceroy tulip bulb sold for 3000 - 4500 florins; a skilled craftsman made 300 florins/yr [1]. Assuming that a skilled craftsman would make at least $50k/yr (probably more, given that $50k is near the median US income), one tulip bulb cost $500k - $1 million. Not so different from selling cats for $500k, so you cannot attack the example for unreasonable prices (s/(dog|cat)/tulip bulb/). Now, was it worth that price? No, hence why it fell back to a much more reasonable level shortly afterwards. But during the mania, selling one tulip in exchange for two lesser-valued tulips would be quite valid.
You missed the point of the illustration, which was that price (market cap) has no relationship with value. Admittedly, the illustration was rather opaque.
That said, I do agree that GDP and market cap can't be compared in a meaningful way.
It's like saying that the ISS is about the size of a football field. Does this comparison help you to visualize the size of the ISS? Sure. Does this comparison help you to understand anything else about the ISS or football fields? No.
No it doesn't, not in a functioning public market.
Just because the guy claims the cats are $500,000 each, doesn't actually make it so. The sole thing occurring there, is a person is claiming something (that is obviously false). No taxing authority on the planet would assess those cats at $500,000; no professional auditing firm would either. The entire bogus premise collapses instantly upon scrutiny.
In almost any market, a claim is worthless unless you can eventually cash it in for a large portion of that sum, typically in a currency that possesses real value. In your example, your cats can never be cashed in for a meaningful fraction of their proclaimed value under any scenario. I can sell my Tesla stock however, there is an extremely well established and accepted value placed on it. I can still pretend, and make an outrageous claim on what my Tesla stock is worth ($1 trillion!), however it is nothing more than a bogus claim and has no actual bearing on reality.