He rejects good ideas and greenlits his own terrible ideas.

If I had to guess what his real responsibilities are now, I'd say he's an ambassador for Nintendo that also mentors younger developers, works on individual projects (like Star Fox Zero) if he wants to and oversees some of the company's interests outside of gaming. It seems like decisions concerning software going forward are going to be decided by Shinya Takahashi, Katsuya Eguchi and Yoshiaki Koizumi with Miyamoto maintaining some influence over projects.

Ten thumbs up!

He is the boss of his own world and is actively looking for a successor

Yeah that guy.

He's the boss, everything needs to be green ligth by him.

He screams at developers now. Man has a serious temper problem. He approves ideas. Looks over their shoulder. Serves on the board and collects paychecks.