Welcome to Fluther.
My own impression from reading this is that the “thousand injuries” was a hyperbolic way of saying “I just don’t like this guy”, and that leads to a “justification” for such a heinous murder. Obviously, the character committing this awful crime is unhinged, and the “thousand injuries” is reflective of that. The actual “injuries”, insults, slights, rivalries, etc. may have existed only in the character’s mind.
At the time of the writing, even though duels were outlawed, a duel would have been the normal way to settle a single grievous injury, such as a public insult, for example. Poe’s character has to justify this particularly vicious way to dispatch his rival – at least in the character’s own mind, so the reader can fathom why the following events would occur – to have the story make sense. Because without “a thousand injuries” (or at least the character’s presumption of “so much wrong done to me”), it’s just a story of a monstrous crime with no basis.