Well done. I had the first of the Genji series mainly because I'd written a story based around the real Yoshitsune. The real Yoshitsune was a badass and wasn't played by Elijah Wood. And Yoritomo was a giant prick, who later sentenced Yoshitsune to death, leading to an epic standoff between Yoshitsune's supporters and Yoritomo's huge army, ending in epic deaths for Yoshitsune's supporters, Yoshitsune offed himself after dragging one last enemy into the burning palace, as the story goes. Anyway, yes, it was basically kill the Heishi because big brother says so, and Yoshitsune was really good at leading his soldiers to do it. They were really no more evil than Yoritomo, but the Heishi killed their father, who had killed Heishi people who killed Minamoto people blah blah blah. Yoritomo had Yoshitsune go on to kill anyone who went against him, including their cousin, Yoshinaka, and as a reward, Yoritomo told Yoshitsune to piss off and die.
If the above was too long: real Yoshitsune was super badass awesome, the world will have to wait until Japan lets one of its decent games with Yoshitsune be let out for us to see. Yoritomo really was a prick.