IIRC, there are some single player activities that don't involve fighting, but yeah for the most part it's all fighting. BUT, the fighting is really well done. It doesn't feel violent because you're not "killing" other players. The more you hit another player the further they fly when you hit them the next time, until you knock them completely off the board which is the ultimate goal. And the more you play, the more characters you unlock adding to the replay value.
But in addition to the standard fighting, there's double-jumping, and all kinds of crazy items to pick up, including bats, laser swords and poke-balls that let out a pokemon to hurt everyone else on screen but you. And some of the levels have their own quirks like rotating floors, disappearing blocks, and a playing field that complete recreates itself over the course of the fight.
And some of the strongest characters, in my opinion are also the "cutest" ones. I can rock with Pikachu, Kirby, and Yoshi. And each has their own special ability which makes picking a favorite character to play with a lot of fun. For example, Kirby can suck in other players and gains their "hat" and one attack ability from whichever character you sucked in. Pikachu can summon lightning bolts and Yoshi can "eat" another player and "poo" them out into an egg, stunning them for a few seconds.
Anyway, I'm rambling. Definitely the most fun I've had playing a game with friends of all age, sex, and gamer skill level on the Gamecube. Can't wait for the Wii version, personally.