In the story we’re told in arc7, the first manifestation of something like a gameboard was done with Yasu reading “And then there were none”. While reading it, Yasu portrayed her imaginary friend as taking the role of “Owen” (which, may be worth mention, has absolutely no relation to Beatrice or Rokkenjima in any ways, but that didn’t stop them), the villain of the story, but also in a way the writer challenging them. Meanwhile Yasu played a “detective game” trying to solve it, and do the same thing Battler did (deny the magic interpretation). One interesting thing there is actually that there is no “magic interpretation” in the original story. Both the “gamemaster” and the “interpretation showed by the gamemaster” lies entirely in the hands of the “reader”. Consider with this things like how Ikuko and/or Featherine wants a “reader” (Ange) in arc6.
For all we know this is simply what’s going on. The gamemaster is in a way an embodiment of the writer but only as portrayed by a reader while they are reading it. It’s not much of a stretch to imagine the story is weaved in multiple levels. That is you have a writer writing a story, and a reader interpreting it and saying comments, and then the reader’s impressions and thoughts and suggestions are then written atop of the story as presented. It’d be as if Yasu decided to write the story of “her game with Owen” which she had in her mind while reading it, and somehow altering the actions of the main character or adding one in order to fit that. If anything I think it’s really hard to make sense out of Erika in arc5 without considering this is what’s going on. It’s a reader who read a story and decided to self-insert herself as a Mary Sue that would completely solve it. The difference then with “and then there were none” is that the stories don’t give out the answers and so someone who knows them is able to completely invalidate the Mary Sue ness of Erika. After all even if Battler discovered all the truth he had to be recognized by Lambda Delta in order to achieve gamemaster rank. If Lambda Delta, being the gamemaster of arc5, can be considered an embodiment of the writer of that tale, it would suggest that what happened is that the author aknowledged that another reader (Battler, or whoever/whatever Battler represents…), one who hadn’t played the role of “reader written atop” for this one tale, had reached the truth and was qualified to speak about it. “It’s now your turn”.
I think it’s not too different from the relation of Yasu who solved Kinzo’s epitaph and now becomes the person who asks that riddle to other.
Still going back to the core question, this could imply that at least in general Beatrice is only the way the author is perceived by the reader. I don’t think it’s too hard to imagine Ryuukishi being imagined as a meta-character himself for instance that, say, when saying things in an interview or whatnot ends up influencing that depiction… and due to “word of the author”, this could even explain where the red comes from to begin with…