I agree that having an unhappy ending is not necessarily nihilistic. I enjoy horror films, for example, and while I prefer those with somewhat happy endings, some of them do end on bleaker notes for the specific events happening onscreen. Some specific situations in life don’t have happy endings, and there can be something cathartic about acknowledging that and “mourning” it through the arts. It doesn’t mean that there’s no greater meaning to life, though. It’s just that sometimes, even if ultimately God is in control and “all things work to the good of those who love the Lord,” sometimes that only fully reveals itself in the next life. There is tragedy, there is death, there is loss. It’s not the final word, but sometimes it’s still pretty imposing. And almost everyone has at least one significant situation where things ended or seem to permanently stand on a bad note. So we can relate to characters and plots where that’s the case.
That said, I don’t like films that are too bleak even if not technically nihilist. Being too bleak and depressing can carry problems of its own, even if it technically isn’t nihilist. It’s hard to say where that line is, but I think cynicism in art is probably often just as unhealthy as nihilism, and some works that technically avoid nihilism still fall into cynicism or morbid pessimism. Even then, in some contexts, some level of bleak melancholy and pessimism can just be realistic and give people who are IN those kinds of sad situations something to relate to. For example, The Scarlet Letter is at times a pretty cynical and pessimistic outlook on the prospects for life for an adulteress in a Puritan town, but it’s realistic and anyone who has ever been scared of being shunned or made into an outcast for some mistake can relate to it. For people in those shoes, stories like that can make them feel like someone understands their position, so they can feel less alone by reading it. So it has its place, it just has to be done carefully and with good motives, I think.