I see the point you are making in this topic and agree that if you analyzed all fiat money around today you will ultimately find that force is ultimately the defining feature that gives today's fiat currencies value. However, pursuing my hypothetical scenario further, what if this same said organization also forced people to pay a different tax that was mandatory and that could only be paid in gold and the tax revenue paid in gold was used to fund the enforcement of various government imposed monopolies. This said organization which is clearly a government that imposed monopolies by force could also still issue the head tax coins that nobody was forced to pay, use, or accept. Would these head tax coins still not be considered fiat money?
Yes. In that case, and only in that case, that gold money is fiat money.
The thing is governments try to avoid using gold as money because they can not print it. They only adopt gold as fiat money, because gold is what people was alreaady using and it is a way to get people used to a government money monpolly. Then later they go slowly breaking the tie with gold. History is a bit more complicated than this, but it is a good basic idea of what they do.