Erm, red-black trees don't have a derivation from gambling terminology either. The wikipedia article says:
In a 1978 paper, "A Dichromatic Framework for Balanced Trees",[6] Leonidas J. Guibas and Robert Sedgewick derived the red-black tree from the symmetric binary B-tree.[7] The color "red" was chosen because it was the best-looking color produced by the color laser printer available to the authors while working at Xerox PARC.[8] Another response from Guibas states that it was because of the red and black pens available to them to draw the trees.[9]
Left-right tree makes no sense. It doesn't distinguish the rbtree from its predecessor the avl tree. I don't think it's helpful to rename a standard piece of computing terminology unless it's actually hurting us to have it. Obviously if it were called a "master-slave" tree, I would be in favour of renaming it.