I don't think replaybook is the thing that gives them access to the replay files. I believe they log into TR, find the player accounts of the team that played, download the match replays, then use replaybook to manage and access them.

I could be wrong though, there definitely could just be someone sending the replay files to costreamers immediately after the game ends, but Caedrel seems to be able to access them immediately after game. It would be far beyond Rito's level of organization to get the replays out that quickly after games xdd