Dominoes:
I'm not certain that a full 724 set of Dominoes is needed. In plain text, the orientation of a domino would seem to be a matter for the font to specify. The orientation becomes a concern only when the dominoes are laid out as played, and that cannot be represented in plain text. If instead of providing all four orientations, no preferred orientation or only a single orientation were specified, then instead of 724 characters only 191 characters would be required to represent the same variety of dominoes as the proposal calls for.
The examples in the proposal show that there can be a semantic distinction between the two horizontal orientations of the same bone. This suggests that if the orientations are encoding separately they should have the Bidi Mirroring property. Your suggestion of encoding the pips instead of the bones would eliminate that problem, of course.

