Hi and welcome to the Forum. That's quite a challenging question!
I assume because you say "game" you're excluding kiddie racing cars and motorbike rides of the sit-on variety.
I think we can also exclude those steering games in which the "car" is represented by a ball-bearing (see
Super Steer-a-Ball).
A distinction also needs to be made between the pure mechanical racing games and the "racing while steering" games that are the true precursors of the modern arcade race simulators.
The mechanical racers usually required two players to crank two handles as fast as they could in order to advance the racing models in competition against each other. These fairly unsophisticated mechanical games date back to the turn of the century and the models were usually horses, sometimes dogs, cycles and later (occasionally) cars.
To complicate matters further, there are also racing games in which the machine runs the races and the players just bet on the outcome. We'll also exclude this type of gambling machine from our survey.
I think it might well be that the first versions of car racing and driving games were British. Innovation in these types of skill and amusement games was strong in the UK during the first few decades of coin-op development. But without further research, a definitive list such as you suggest is impossible. At present our slot machine patent listing is incomplete and many games weren't patented anyway. All we can do for now is list some early and interesting examples.
Algernon Evans's 1928 Patent No
GB322268 for a rolling road type driving game is the earliest I've seen. It's certainly a fascinating early effort - complete with scoring dial, natty driver's chair and massive oak cabinet containing a large rolling drum only a small part of which is revealed through a narrow aperture in the front. Although the patent was filed, no sealing fee was paid, which makes one wonder whether it made it to the production stage.
Three years later Mark Myers filed Patent No
GB368974 on a very similar idea. Called the
Road Test, the player steered a metal toy car (or cars) along a road (or roads) laid over a large rotating metal drum. If the car strayed off the road, a circuit was made which caused a gauge to register the error. Only when completing the course without incident was the coin returned. The steering wheel was the only control; players could not alter their car's speed. It must be the most successful early game of the type.
Myer's claim is for the mechanical and electrical linkage between the steering wheel and the car, not for the rolling road concept which already existed, as he acknowledges in the patent.
He followed this with
Double Road Test, in 1936, which allowed two drivers to compete against each other (the 1931 patent anticipated this version). A very similar game was also made (possibly under licence) by Ruffler & Walker.
Charles Ahrens also made a single player rolling road game called
Steer-a-Car. This looks a little earlier and does not employ Myer's electro-mechanical linkage. Ahrens was not known for innovation. He had several legal run ins with other manufacturers for stealing their ideas, so it's possible this imitated an earlier design.
On JG Brenner & Co's
Drive-A-Test (early to mid 1930s), a paper roll-fed map served as the rolling road, a section of it being dispensed as a record of the driver's skill.
The Germans also appear to have been active in the late 1920s or early 1930s, designing a number of "table top" style steering and racing games.
The Americans started to make versions in the 1940s. Notably the
International Mutoscope Company's Drive-a-Mobile (1940) which added a light-up indication of the player's position on a map above the rolling road. The following year, the same company produced a two player version called
Cross Country Race.
Their
Drive Mobile of 1954 included a driver's seat.
Their weirdest "rolling-road" steering test was the space-age
Flying Saucers.
Although these early electro-mechanical games sometimes combined driving and racing, for the racing games proper (with accelerator pedals etc.) we have to return to America and the arrival in the 1950s of Capital Projector's
Auto Test which replaced the rolling drum with a rear projected street scene which advanced behind the model car.
This became the format for the next couple of decades. Gear levers, brakes, driver seats and realistic sound effects were added and the steered vehicle could be anything from a car, motorcycle, jet, rocket or submarine.
The two player
Turnpike Tournament, an early 1950s machine, used 8mm movie footage of roadways with traffic. The steered model cars sat rather incongruously against the screened street scenes.
These rear projection games usually incorporated a timer and more emphasis was placed on speed, although dodging obstacles remained important, of course. Chicago Coin were the biggest manufacturer from the late 1960s into the '70s.
Britain's M1 motorway opened on on April 11th, 1960. Before you risked a run on it, you could test your skill on the
M1 Road Test, a revamp of the Mutoscope
Drive Mobile (This example still operates in Mablethorpe). A variant of this machine was
Brighton Run.
Williams Road Racer still used the antiquated rolling drum system in 1962.
Parallel to these were some more quirky racing car design concepts such as the coin-operated slot car racing games. For several reasons, including technical problems, these never really became mainstream. See:
Genco Motorama, 1957
American Machine and Foundry Little Indy, 1960s
Southland Engineering Speedway, 1963
Southland Engineering Time Trials, 1963
American Machine and Foundry American Indy, 1967
ICE Turbo Drive, 1980s
Motorcycle simulators were very rare until the arrival of video technology.
Bill Kurtz's
Arcade Treasures and
Slot Machines and Coin-Op Games are the best sources of information about games from the 1940s onwards.