Maxi.... I think you missed maybe a little of, no, most of, no, all of the context of my post. The point of replays are to let people watch the match as a spectator AFTER it has been played via recorded data. Play, pause, watch from another angle, any angle, another player, rewind, fast forward, slow motion, high definition renders, commentary, etc.
You would have to record the data a spectator client would see, perhaps a little more. Then others can later access the data and replay the match. Perhaps even start watching the match before it ended. If your replay server is separate from your game server, there would be no lag bleedover.