If you observe the "dots" (1-4 dots) and some fields, which are marked with i, ii, iii and iiii instead of 1-4, you get that, what is marked green, blue, yellow and violet. The 4 corners (each with dots) seem to present a starting field, the 4 middle sectors seems to present, where the game figures finally should end, if successful. It seems, that 4 four figures are destined to arrive there, cause there are 4 positions (as in Mensch ärgere Dich nicht).
There's a wall in the middle between start and destination fields (different to Mensch ärgere Dich nicht). Possibly the game rule had been, that you first had to cross the "wall in the middle", before you could advance to the destination fields. In the normal case you possibly had to run once around the field, to reach that field, where your color could cross the "wall in the middle" ...
... though there might be an error in the representation. The door for "green" (in my modification) is missing, and the door for "blue" is possibly there, where the door for Green should be, and the blue door should be, 90 degree in counterclockwise direction.
Then there are 4 fields in the wall section , which possibly shorten the way of the running, if the figures can reach this field (they are marked with a cross) ... a similar way to shorten the way appears in the Korean game of Yut-nori ...
... which is played with 4 sticks instead of a die (with the results 0-4). The result of one stick is either 1 or 0 and the ways you have to go are like this ...
All these points look relative logical, if we assume, that the figures had to run always more or less equal to counterclockwise in each move, and never in direction of the clock.
Maybe there had been other ways to break through the wall ... I don't understand the other dots on the middle wall. Also I don't understand the function of the two crosses at the left border.
Well. If you've crossed the wall, you likely had to run around the middle for a second time, so I imagine. You couldn't go directly to the destination fields.
Somehow like this for the run of the color "yellow" ... if it didn't happen, that the figures found a shorter way through the wall by luck.
Well, only a suspicion.