I think it's an exaggeration to say this event was the end of the company. E.g. we don't say GM ended because it went through a bankruptcy.
Kongo gumi still continued operating even though it went through a restructuring, so it's fair to say it's still the oldest company in the world.
Just it's no longer the oldest family business in the world - that ended when direct Kongo control of it ended, although I hear they still have a ceremonial involvement with the company.