I have an idea on how you can make this,
This will be in 1st person perspective. (So basically like you are in a real car)
1. Make a HUD that looks like an inside of a drivers seat in a car.
2. Remove the current player soundset. (You can add a custom one that sounds like a car)
3. Disable jumping.
4. Make or modify a car model and make it so that it has the properties of a character.
5. Give it a waypoint around the track.
6. Increases it's speed if you want to.
7. The check points could be like objectives. Set a item (or a win zone) anywhere and in the settings change "isobjective" to 1 and so on.
Done?
NOTE: I don't know if this will work. Since I have not attempted or done this kind of thing, I cannot guarantee anything, Since I suck at modelling, scripting etc.. But this is what I think can be done to achieve a basic 1st person racing game.
If you can see the enemy, they can see you.