Cryptocurrencies aren't worthless though. Computationally expensive, cryptographically useful numbers are a valuable commodity. They are valuable in virtue of the computational work that they make possible, the same way that electricity or silicon are valuable in virtue of the computational work that they make possible, i.e. successfully, verifiably lengthening the blockchain.
> Fiat money is money that is in itself intrinsically valueless but that is accepted as money because the government says that it must be...require that it be accepted as money (emphasis added)
There's the part where you say it.
> The only difference from most other fiat money is that with cryptocurrency it is not a government declaring it to be money. It is a large group of people.
And there's the part where you take it back. As you started to say, declaration is a necessary but not sufficient condition for fiat; it also requires forcibly maintaining the declaration. If a large group of people have that power then they're effectively a government, making "non-government fiat currency" an oxymoron.
Fiat money is money that is in itself intrinsically valueless but that is accepted as money because the government says that it must be. It has nothing to do with whether or not it can be printed (or otherwise easily created).
If a government were to make a cryptocurrency like Bitcoin their legal tender and require that it be accepted as money, then that cryptocurrency would become fiat money.
Money has for the most part been a dichotomy: commodity money and fiat money. Bitcoin doesn't fit fully into either category, but it actually is closer to a non-government fiat currency than to commodity currency.
Commodity money was things that were valuable themselves, independent of their use as money. Gems and precious metals, for example, are useful for making jewelry and for other aesthetic purposes, and their rarity makes them useful as status symbols for upper classes.
In societies that do not use them for money, people still want them and use whatever is used for money to buy them.
Cryptocurrency doesn't really fit as commodity money because the demand for it is almost all for its use as money. If people did not accept cryptocurrency as money, I doubt many people would be interested in buying it.
As money, cryptocurrency is much more like fiat money: something worthless that has been declared to be money. The only difference from most other fiat money is that with cryptocurrency it is not a government declaring it to be money. It is a large group of people.
We probably need a new category, non-government fiat currency, to cover cryptocurrency as money.