Initial D Gaiden

Story mode lets you choose between 4 characters, depending on which story you select, it follows the main parts of the manga (like Takumi racing against Ryosuke for example) or not (Natsuki's story for example does not follow the manga at all, as she's not a street racer to begin with).

Initial D Gaiden is the first video game in the Initial D series for Game Boy.
The game was only released in Japan.