As a PhD in Math, my opinion is that 0 is a number. Most language have special words to use when the amount is 0. For example, instead of "Five persons want to eat cake." you usually say "*No one wants no eat cake".
https://en.wikipedia.org/wiki/Presupposition
It's also a thing in mathematics.
https://en.wikipedia.org/wiki/Syllogism#Existential_import
The statement "How many blue cats are bouncing" makes the presupposition that blue cats exist. That's just how language works.
It's one of those things where a formal education in mathematics will teach you to think about a thing in a way that is actually unnatural to most human beings.
The standard example that linguists use is "Do you still beat your wife?" to which you can answer neither "Yes" nor "No". Answering "Yes" means you admit that you used to beat your wife and that you are still doing it. Answering "No" means you admit that you used to beat your wife but claim that you are no longer doing it. You can only answer by escaping to the meta-level and attacking the presupposition as in "I am not currently beating my wife, nor have I ever beaten my wife". If you're a politician, then even that will get you in trouble. (Not thinking of a pink elephant, and all that, ...)
If someone ask "How many elephants are in the fridge?" it would be weird.
I don't think that it is unnatural to answer "zero" in the first question, it is probably a social convention. For the second question I agree that is unnatural.
This is not po-tay-to po-tah-to, people. It's a real thing.
Most people aren't arguing this. Most people are discussing colloquial understanding of language and discussion. The differences you are arguing are important in a highly specialized area of math and science.
It feels like you're arguing whether an object is a Boeing 737 or an Airbus A320 when the important point is an airplane is not a car.
Actually, I think they're arguing that it would be useful if more people understood this. In addition, the point of the game was to teach logic, not a colloquial understanding of language, which every child gets growing up anyway.
I was recently writing a function that returns early if all items in a list meet a certain condition. It was interesting to think about what should happen if that list is empty.