"Intent" is a defined legal term and intention is not necessarily required. In Texas, for instance, there is a False Report offence the relevant portion of which is:
...knowingly initiates, communicates or circulates a report of a present, past, or future bombing, fire, offense, or other emergency that he knows is false or baseless and that would ordinarily:
(1) cause action by an official or volunteer agency organized to deal with emergencies;
The "knowing" culpable mental state means you must at least know that your conduct is likely to produce the result. If I tell my wife I'm going to dive at such and such place and will return or if it's understood that I always return, I know that if I don't return by, say, dark, she's going to activate some emergency services. There's a principle of responsibility called "causation" that says if I cause something to happen that wouldn't have happened but for my action, it's as it I did that thing myself. So the "initiates" part could be fulfilled, because I caused my wife to make the false report by my act that I knew likely would cause that to happen.
Now, if I tell my wife I'm going to work, and she finds I didn't and calls the police, it does not immediately become an emergency. As an adult, I can disappear if I want to and be voluntarily missing. In the US at least, an adult cannot be entered into the missing persons database unless it can be shown that they are likely endangered (senile, suicidal, was being stalked, etc.). I don't have any reason to believe that I will instigate an emergency response, so I'm not culpably knowing. But when I said I was diving, that changed things, since I certainly know what that will trigger.
I suspect that, unless it becomes clear that the guy was meanly trying to torment his wife or do some other malicious thing, as opposed to being mental in some way, he won't be prosecuted. The charge can be a legal and convenient way to get him into treatment, once he was found.