I played a rough game with my girlfriend once (she didn't have enough cards for a full game). Apparently, major characters from the show were your "hero" cards, and you would use the monster-of-the-week cards to attack one another. Like how Magic: the Gathering uses creatures to attack the players, save that I think you could have more than one "hero." As I said though, she only had so many cards.
And Jan-Ken-Pon is the Japanese name for Rock-Paper-Scissors, though Helvetica Empress may have known that already.
Oh, and I believe that the card game was made by Guardians of Order. They are the ones who made Big Eyes, Small Mouth. The Sailor Moon RPG, which has similar but more complex rules than the card game, was the first major BESM product. And yes, I played that with her as well.
My character was the Solar Sheriff... At least I got guns.