Buff guy and Kitty guy run around and kill things. Kitty guy swings on Buff guy's sword. Things die.
More seriously, Golden Axe III is one of the sequels to the original Golden Axe. One notable change is that players can now pick several different routes through the game by making choices at certain intersections. Also, the two players can use a "team-up" attack for high damage, which is used very frequently in this movie.