That is called a spanner head bolt. I have a set of IKL dining chairs for Selig which have this same bolt. While you can certainly buy a spanner head set with various distances between the points, it may not be worth the cost (and additional tool clutter) since you don't need those bits very often.
Two alternate options are:
1) thin needle-nose pliers, or
2) take two nails (or ends of a paper clip), tape to a coin to fit the distance between holes, and presto . . . instant spanner wrench.
Almost all of the Selig "walnut" chairs are stained beech. There are a few designs that used solid walnut.
The first photo you uploaded shows the top coating flaking away (some type of lacquer I think). So that usually indicates stained beech for the Selig pieces, unless someone did a DIY lacquer effort afterwards.
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