(From the Introduction in the rules.)
Regimental Chess is ... a battle by a division of chess pieces on a (board) three times larger than traditional chess.
Each side has 14 infantrymen (pawns), 4 bishops, 4 knights, 4 rooks, 2 queens, and a king. Pieces may move individually or in battalions. A battalion is the group of each piece type, e.g. 4 bishops are a battalion. Battalion movement is all pieces making the same move (e.g., three diagonally northwest). It's like station keeping in naval fleet movement. Or battalions can move in a chain, each advancing forward to take the place of the other, like marching forward. All pieces have to spaced apart equally for chain movement.
It was a commercially available game. The map provided was a roll up chess board. The pieces were of good quality plastic in the traditional Staunton chess piece style.