Fiat currency does not have to be issued by a government, and does not have to be legal tender. And Bitcoin certainly meets one of the "various" definitions given in the Wikipedia article. There are plenty of other definitions of the term it meets -- at root, a fiat currency is simply a currency whose value exists because someone said so, rather than because it's tied to something else. And... well, Bitcoin has value because people say it does, not because it's tied to something else.

It's part of the definition of "Fiat currency." i.e. It's issued by fiat[1].

[1] fi·at

ˈfēət,ˈfēˌät

noun

1. a formal authorization or proposition; a decree.

But that's true of a good portion of currency. The USD became a fiat currency in 1971.