I wonder if the creator of Nimmar was inspired in part by Kokusai Sannin Shogi. In both, a person wins either by checkmating all the other players or by getting their "king" to the centre square. Also in both, the pieces aren't named the way most shogi or chess pieces are named, but are instead called after political concepts and non-war-related things, like "temple" in Nimmar and "Colonist" or "Propaganda" in Kokusai Sannin. (EDIT: I haven't played many chess-type games with more than two players, however, so for all I know, the former is just a common characteristic of this type of game.)

Also, I found this in the Wikipedia article:

If two players start the game as allies, the remaining player is automatically First.