"Racer Mini 4WD - Japan Cup" - "Racer Mini is a trademark of Tamiya"
Tamiya is probably the biggest radio control manufacturer in Japan; they've made lots of popular cars. The Mini series they made started a short-lived craze in Japan which led to this game. Minis, which are about 6 inches in length and run on 2 AA batteries, were actually pretty simple. All there was for a control was an on/off switch. After that you put some special bumpers with rollers on the car, and put it on the Mini racetrack.
The track was made of individual lanes for each car with plastic walls separating each car. The bumpers of the car would run along the walls and guide the cars around the track. So basically, the point was to get your Mini going as fast as possible without making the car jump the track. A ton of aftermarket parts and stuff were available for the Minis, but the craze died down quickly. These were sold in the US as well but didn't really catch on here.
Other companies tried to sell similar cars here... Hot Wheels included. One of the manufacturers toured the country putting on races, and even had a TV show for a little while (hosted by Jesse "The Body" Ventura).
Anyway, with this info in hand. I can now say that it sounds like a kind of stupid FC game ;) Nice label, tho.