He's the president. I'll rename him to prime minister in 0.2. Who would the Vice President be? She's his aid.
AFAIK there is no "Vice-President" equivalent to a Prime Minister. You have the Head of State (in Japan, this would be the Emperor), the Prime Minister (the guy who is actually in charge of running the country), then the Cabinet, made up of various Prime Minister appointed Ministers. These have various roles such as Minister of Defense, Minister of Finance, Minister of Foreign Affairs etc. The Wikipedia article about the
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has a bunch more info if you want to go in-depth with it.
If you want the Prime Minister to have an assistant or helper for his actions, you could just call her his personal assistant or something, I don't know the actual role. Considering the plot, you could even call her something like the "Minister of Procreation" or "Minister of Population and Growth" or some such.
Beyond changing President to Prime Minister, and avoiding having a vice-President (or something weird like a "vice-Prime Minister"), I don't think it's too important be super accurate with the Japanese political structure, considering the type of game it is.