I'm wondering, is a character dying in a story mandatory for a good story?

Nope. Dracula is a darn good book, but then so is Racketty-Packetty House. 🙃

Character deaths are automatically pretty intense, and they open up new possibilities for the types of themes you can explore (and how deeply), but the world of story is a wide and deep sea with all sorts of interesting things floating in it.

The author's job is to pull some of those interesting things out, arrange them effectively, and make worthwhile comments on them. There's room for all different tones and scales and levels of complexity. You don’t have to have a death any more than you have to have star-crossed lovers.