Actually, I think that they don't really need the replay mode. The game does have enough information to know what mechanic killed the player or what mechanic the player is closest to that he has survived or got hit by. So really, the easiest option would be when the player dies, they have some kind of UI option that lets them click and see a small mechanic explanation on the thing that led to their death. The way it would probably work is, if you survived a boss mechanic, but then an auto attack finished you off, the UI element would display the boss mechanic that put your life low enough you died to the auto.

That's probably a better option because the video recording would require more data and it doesn't really help all that much since what the server sees might not be what you see. So a quick visual snippet is better-ish.