Just happened to come across this word in a dictionary, and I was like, “wth?” I don’t know about you, but when you see just this word for the first time without any explanations or translations, you’re most likely thinking of anything but “government”. The first thing that probably comes to the mind of a somewhat advanced learner is that this word literally reads 祭り事 matsurigoto,festival.
The Chinese character that was assigned to this word should remind you of 政治 government, so that takes of care of that. Still, what’s up with the actual Japanese reading?
Once we look it up, we’re reminded of the fact that etymology is often intricate and complex, based upon things that were common or common-sense to the people of a certain period of history. And also, that often, when you think about it after you’ve looked it up, you’ll think “makes sense, it could really mean that.” But you couldn’t even begin to figure out the meaning beforehand.
But I disgress. The answer you’ve been waiting for: According to the Meikyou Kokugo Jiten, festivals did play an important role among the men in power, thus festival, feast was used to refer to them.
Huh. Surprisingly simple explanation, don’t you think.
PS: Another dictionary elaborates, the worship (matsuri) of kami (Japanese deities) was a major feature of Old Japanese culture. Executing the will of the kami was the official justification for ruling.