Well, I have finally tried the ancient Chaturaji with oblong dice:
https://www.ajedrezeureka.com/chaturaji (this is 1v1 both owning 2 colours).
It's just a game for kids (or drunk adults) with no much skill involved, still funny to try by the way.
....
Another historic 4-player version - that uses the ancient movements of the pieces and was playable without dice - is the Acedrex de los quatros tiempos = '4-season Chess'. Each player owning: King, Rook, Horse, Elephant and 2 pairs of pawns, oriented on 2 different directions.
1. I do really like to play Chaturaji on Chess-dot-com, the name just means "4 Kings". I like this game better than the 4-Player Chess on that gigantic cross board.
2. This is not the original, truly ancient, Chaturaji. That used dice and had Elephants moving like Rooks (in place of Bishops) and Boats on the 4 corners moving like Shatranj Alfils.