Can you identify this likely chess variant?
Michael Ireland, the person who posted their copy on chessvairants.com, remembered some details, and replied with some added information (original post here). I will quote it here:

Viking Chess Rules as best as they can be remembered – November 28, 2020
The goal of the game is to checkmate your opponent's king as in regular chess.
Board: The board is made up of &quot;rings&quot; linking &quot;crosses&quot; (the spaces).  There is a centre &gt;space, the “star”, in the middle.
Pieces: There is a king, 2 rooks (flat tops), 2 bishops (spikes) and 4 pawns per side.
All pieces start off the board.
On their first turn (white goes first) each player places their king anywhere on the &gt;board on any space except the centre space (I believe that no piece could start on the &gt;centre star because it gives too much of an advantage to start there - but I am not 100% &gt;certain of the rule).
In the second and subsequent turns, each player can either move an existing piece on the &gt;board or bring another piece onto the board as per turn 1.
Different pieces move differently as follows:

Pawn moves one space in any direction
Rook moves up to 3 spaces up or down, or one space to the side
Bishop moves up to 3 spaces around one of the rings, or one space up or down.
King can move up to 3 spaces in any direction up or down

Once placed on the board a piece can enter the centre space or through it.
A player takes an opponent's piece by moving a piece into their opponent's piece's space.  &gt;Once a piece is removed from the board it cannot return.  I do not believe there is a &gt;rule to promote a pawn to a Bishop or Rook.
The King is the strongest piece on the board combining both the Rook's move (3 up or &gt;down) and the Bishop's move (3 around a ring in either direction).
If the King is taken/mated the game is over.