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"One note: Ancient games often used dice. Would such be a part of this
game?"
Based on what you've laid out, absolutely. And I totally agree with the
pyramids being blocks; that's exactly how I saw them when I looked at the
pieces after reading the article. As moving pieces, wazir to R3 is all I
could see them as... although orientation could be important. The pyramid
shape could have 2 distinct orientations in a square, and would thus block
or deflect left or right. 

You might use a few kinds of racing pieces, and throw a few dice,
apportioning results of the die rolls as you see fit. It might be nice to
have fewer dice than pieces, to make the choices more interesting. If you
can move a block out of your way and/or into the other guy's but it costs
you a move elsewhere...

On the other hand, looking at the center and lower left of the picture, I
saw pigs, dogs, truffles and baskets. So I'll stop there, and let someone
else have at it next. Enjoy!