I’m not gonna bother with saying that the other losses that you’re discounting can be just as tragic as losing a romantic partner. Everyone else here has said it probably better than I could.

What I’ll bring up is that not only are there more kinds of revenge motivation than the loss of someone close to you, there are more motivations than just revenge. For other kinds of revenge, what about wounded honour? A hunter who’s prey keeps escaping them might feel the need to finally end that hunt before they can look themselves in the eye. That’s its own form of revenge arc, and it can make just as powerful a story as avenging the loss of a loved one. And for non revenge motivations, there’s far too many to list, but here’s a start

• duty
• repaying a debt to the world
• self improvement
• survival (usually more of a side character motive compared to a hero protagonist, but still good)
• seeking admiration (from people in general or from a few important people)