Yeah, Masakado is an optional boss who gives you a new Magatama for defeating him in the Bando shrine.
I was pretty sure that Izanagi & Izanami were in the older games, but now that I think about it I'm not entirely sure.
Erm... I believe you don't actually fight Masakado. If I remember properly, you have a bout with each of the four guardian Kishins, and then you fight Bishamonten. After that, Masakado shows up and gives you the Magatama.
Yes you're right! You don't fight Masakados, he only gives you a Magatama once you reach his place, if you're talking about Nocturne of course. But I don't know if you fight Masakados in Shin Megami Tensei II, I haven't play it too much, so I can't say.