Anyway, since the Red King IS a chess piece, he could easily be called "Chess Piece Face." As for the rest of the song:
"What's going to happen to Chess Piece Face?"
Is he going to wake up, or what?
"There go I, but for my face."
I don't entirely understand this line, but it could be referring to the disappearance of the narrator that would occur when the Red King wakes. I don't know about that "but for my face" part.
"All I know could be defaced by the facts in the life of Chess Piece Face."
If "all I know" is just the King's dream, it could easily be defaced if he wakes up.
"I don't know where he lives Or if he knows to sail Or if little schemes like this one ever cross his trail."
I really can't fit these into my interpretation. Can anyone help?
"But I don't believe he's dreaming Or if he cares to know."
Now, that "dreaming" part was what really made me think of the Red King. I suppose the narrator refuses to believe that he is just a part of the King's dream (like Alice in the book).
"So I shudder in my lampshade"
Now, this is a little awkward, but the Tweedle brothers said that Alice would go out "like a candle." I guess it would make sense for a candle to wear a lampshade.
Now, this was probably not what the Johns were thinking when they wrote this song, but it seems to fit fairly well.