It presumably was made around the same time as Fix-It Felix, Jr., due to its similar graphics. TurboTime was once one of the most popular games in Litwak's Arcade and Turbo loved the attention.
When Mr. Litwak installed a new racing game, RoadBlasters, it stole Turbo's thunder, causing him to become jealous. As a result, he left his game and tried to take over the new one. This caused both machines to be considered "out of order" and unplugged for good. Since then, the characters of the arcade usually refer to a character game jumping during arcade hours as "going Turbo", and is something to be avoided. However, near the end of the film, it's revealed that Turbo had survived his game being unplugged, and had, disguised as King Candy, taken over Sugar Rush.