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Is drawing a line with a crayon forbidden on Shabbat?

There are board games that involve using a crayon to draw lines (not letters or figures) on a board (e.g. EuroRails). Are these activities problematic on Shabbat? There are two aspects: the drawing itself and whether the crayon is mukzah. (Assume that the crayons are part of the game, not raided from the kids' toy stash. So they are only ever used for playing this game.)

The game board is coated such that the crayon marks are wiped off after the game is over; the marks are not permanent.

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