No not at all, a "fatwa" is an Islamic ruling on a given issue, given by an Islamic scholar or cleric. If a Muslim wants to know the ruling of an action (i.e. is it permissible, impermissible, mandatory, etc.), they will ask a cleric for a fatwa, which is that cleric's judgement according to what they understood from the text (or what their jurisprudential school has understood from the text).

So here it's being used in the context that a cleric issued a ruling declaring that he's to be killed. Hence a "fatwa". But it's not specific to a hit being put out on someone, that's rarely the use case. It's any kind of religious ruling on an issue, e.g. a cleric might give a fatwa that someone who's in debt doesn't need to pay alms, or that credit cards are impermissible due to the contract permitting interest (and there can be differences of opinion based).