I am going to have to answer the title question with a definitive “No, dialogue is not necessary for a good story.” There are a vast array of examples. One of the most famous that comes to mind is The Waves by Virginia Wolfe (1931) which is entirely written in the soliloquies of six characters.
The non-fiction genre will more often recount a story and never once give any character dialogue. Consider histories of Civil War battles. There are great stories which never quote one character.
Documentaries - especially ones about nature - can often be done with only a narrator, never entering a single dialogue.
Fiction has had many examples as well. The Slow Regard of Silent Things has a great deal of monologue but no dialogue.
Poetry very rarely has any dialogue. Consider Edgar Allen Poe’s SHADOW—A PARABLE, which has exactly one sentence of dialogue. The epic science fiction poem Aniara by Harry Martinsen is 103 cantos—longer than most novels—and contains 2 verbal sentences.
Dialogue is not needed for a great story, no. Dialogue uniquely applies to stories where people interact in conversation. That doesn’t always need to happen.