Two person wooden peg board game?
It could be a travel variant on a Go board. If you're not familiar with Go, it's an ancient game played by two players, usually played with white and black stones. While the standard size of a Go board is 19x19 lines, 13x13 is a common "beginner" variant.

The main objection to this theory is the number of stones: you usually have enough to cover the whole board between the two players, so I would have expected 84 black pegs and 85 white ones.