For a very simple race-to-the-end kind of board game, you could use the concept of surviving various perils and living long enough to reach the goal of becoming a great, wise Dosu.
Granted, that would involve:
1) Ignoring the fanon that Dosus are born, not made, in favor of the (less-popular?) fanon that any yukkuri that lives long enough can grow up to be a Dosu.
2) Letting any kind of yukkuri become a Dosu--usually, you mostly see Dosu Marisas, but you'd probably want the game pieces to be a variety of types (Reimu, Marisa, Alice, Patchouli...)
3) If you want anyone to actually _finish_ the game, having the obstacles be non-fatal--"You are attacked by a Raper. Abort your stalks and go back 5 spaces to recover," not "You are attacked by a Raper. You die. Game over."
It might also be fun to divide the board up into stages--say, the first stage has events that might occur to a baby/koyukkuri, then once you reach a certain point, you stay there until you roll doubles, representing "find a mate," and then you enter a stage with events that could occur to an adult yukkuri with a family ("Your children turn out to be scum. They meet with JUSTICE. Go back 10 spaces and try again.") The third stage is, I don't know, maybe you're now the head of a clan, with all the attendant problems.
Or you could have the main path be for a stray yukkuri, and then if you're lucky, you could get adopted and move onto a parallel path for a pet yukkuri--but on that path, there are spaces/cards that would bump you back onto the "stray" path. ("Your owner turns out to be drawn by Ayazou. Run for your life and go back to STRAY.")