Gold is money because people strongly desired it for its physical properties and then, subsequently, discovered that it was the most marketable good and thus useful as money.
This is not exact. The physical properties of gold are not that great. In ancient times, many other metals were much more useful, especially considering how strong metals and allows were important to forge weapons. Gold is soft and pretty much useless in metallurgy. After all, we talk about iron age, bronze age and all for a reason. We don't talk about golden age, apart from figurative speech.
Gold indeed had useful properties, but precisely those properties made it ideal as a medium of exchange. It's easy to make gold coins, gold is almost absolutely inert chemically, it's rare and it is easily distinguishable. All this made it the best tool as money. Not because it had amazing properties for non-monetary uses in the first place. It just hadn't.