A similar, ancient game with changed queens move is Amazone chess.
Almost Chess is a good game to play with a chessplayer; it is easy and natural. Perhaps you will get a regular chessplayer interested in chess variants.
Of course, you can play Sort Of Almost Chess, where one side has a normal Queen... (Hey, you know how I am about chess with different armies! :-)
Both kinds of Queen have exactly the same strength, so it is an even game, even for masters.
Note: this game was never published or even mentioned in email until now. I have known about it for more than a year; part of my research into values of pieces...