May be Maricar is the only activity in Japan, which ordinary Japanese cannot participate. Although you have a proper driver's license of Japan, in case you do not understand English, you cannot do it. Actually it written on the doors of their offices that Japanese are not allowed. The reason is simple. The all instructors speak only English and mostly are non-Japanese who does not even understand Japanese!
On the other hand, foreign tourists who have vaild International driving permit can enjoy riding the carts on the streets of Tokyo around JPY 5000. They have several base stations throughout Tokyo and each base station has specific routes to run. One of the most popular routes are the one from the base station in Akihabara district which you run the streets of Ginza district.
Maricar is not related to Nintendo nor Mario Cart. Therefore do not expect to rent costume of Mario there for free! If you want to be as Mario, you have to bring your own!