There are dice roller race games, for example The Royal Game of Ur. There is capture when you land on an opponent's piece from behind, and some squares are safe and give you an extra move.

So what if you had a race game, particularly The Royal Game of Ur, and the pieces are rock/paper/scissors? Like captures like. Some more tactical complexity. Physically the pieces would have one dot, two dots, or a triangle of three dots. A piece with one dot could capture the piece with three dots. Maybe a rosette means an extra move but not safe space. Testing can sort this out.
 

If this actually worked, what should the name be, and maybe theme?

I had thought of red, white, red for the three rows, with a maple leaf for the rosette(s). But that's a headscratcher.