Japanese Games of Note

Nobody seems to have touched this one, so I'll chip in a partial answer about the emperor part. Couldn't get anywhere with the prime minister part of the question, maybe because nobody really cares that much whether the prime minister watches baseball or not.

Anyhow, Wikipedia Japan has an article on what's known as "Tenran-Shiai" a sports event attended by the emperor, not necessarily limited to baseball. The first baseball match attended by an emperor was a night game on June 25, 1959 between, lo-and-behold, the Tigers and the Giants at Korakuen ball park (anybody old enough to remember that place?). This was during the reign of the Showa Emperor Hirohito. According to the article, this is how it came to be.

One night the emperor was sitting in his palace, and noticed bright lights glowing off around the direction of Suidobashi (a train station near Korakuen). He calls an aide.
Emperor: "Hey, what are those lights all about?"
Aide: "Those lights are from a professional baseball night game, your majesty."
Emperor: "A what?"
Aide: "A baseball game, your majesty. Someone throws this thing called a baseball and another person tries to hit it with a this thing called a bat."
Emperor: "Hmm. Sounds ridiculous. The Japanese people must really be going bonkers. I gotta take a look at this."

Well, it sort of went like that. The Giants owner at the time, Matsutaro Shoriki, heard of this conversation and decided to organize a Tenran Shiai hosted by the Giants, partly as a favor to the emperor, but probably more to promote the Yomiuri Giants as the team of Japan. But the imperial palace agency, to their credit, were a bit suspicious of Shoriki's motives, and told him that they couldn't respond to a request from a single ball club, as this would be seen as favoritism. This stalled negotiations.

At the same time, the Pacific League has similar intentions. The owner of the Daimai Orions, Masaichi Nagata, also put out feelers for a Tenran Shiai request.

But in the end, the Giants won out, as they always did in those years. Owner Nagata of the Orions decided not to make a big deal of it, releasing a statement that said, "It is an honor to have the God (ie. Emperor Hirohito) attend a professional baseball game. It would be inappropriate to make a controversy out of such an event."

So it came to be that the emperor and the empress watched their first baseball game. Now unfortunately, there was a rule that the emperor couldn't stay out later than 9:15 (security reasons? past his bedtime?) so he wouldn't have been able to stay for extra innings anyway. But, with the game tied at 3-3 at the bottom of the ninth, Mister Shigeo Nagashima hit a sayonara home run, ending the game at 9:12. Talk about clutch hitting.

For all you die-hard Japanese baseball fans, the starting pitchers were Masaaki Koyama for the Tigers and Motoshi Fujita for the Giants. Sadaharu Oh hit a homer to tie the game, and Nagashima hit a homer off rookie Minoru Murayama for the win. Interestingly, there's some controversy as to whether Nagashima's hit was a homer or a foul ball. Murayama secretly thought it was a foul ball, but decided not to argue because it was a Tenran Shiai.

Westbaystars-san (walking-encyclopedia-of-pro-yakyu), I leave the prime minister part up to you.