This is my favourite article on the subject.

I think the stuff about where the car is going relative to the road is just a small hurdle in understanding, you need to tackle.

There's no direction beyond what you decide to include. No turning unless tou come up with it. You can stick that sprite in the center if you like, but the norm is, as far as I can tell, to push the car sideways in a curve, and allow the player to counter this by pressing in the opposite direction.

poorya79 said:

Just for context, I'm not new to coding.

Very good!

I'm afraid the answer to most of those questions is “it depends”, and there is no good answer to many of them.

How it is drawn depends on the era of the game. Old games (70's, early to mid 80s) were drawn one one scanline at a time. That visual style was common because it was straightforward: draw the far away stuff one line at a time, draw the next line based on what was closer, the next line closer still. What was shown on the screen could be figured out by what is in the distance in the course data, and the orientation of the car on the road kept as separate data. In the 80's and early 90's a lot of graphics hardware was sprite and tile based, so rendering it could have been composed that way. Sprites for the road at various distances, sprites for the flags and the car, sprites for the mountains and backgrounds.

Modern graphics systems have a tremendous variety of ways to emulate the old appearance. There could be huge articles devoted to twenty different approaches and they'd only scratch the surface of the options.

I can think of several ways to store the data, several ways to draw the track, several ways to make the car stay inside the road, several ways to make the flags and rocks and other pieces of data move.

The easiest that comes to mind would just be storing a “turns in the track” array for graphics that moves over time, having the overlay map not being really tied to the data just colored as a percentage of the way through that data, and merely walking down the array as the course progresses. The road would then always be centered and the car's position have nothing to do with the turning of the track data, just a position relative to the screen. If the “turns in the track” data says -1, then the car moves -1 (probably slightly left) during that segment, if the data says +5 then it's a big turn (probably to the right) and the car moves +5 unless the player is turning. When rendering in the distance, you'd look at the next few items in the turns in the track array. If it says -1 you'd have a slight turn to the left. If it says +5 you'd have a hard turn to the right. Each one is sequentially up above the other, to the horizon line, slowly moving down as you progress through the array. But that's just one approach.

um… not sure if anybody mentioned already, but seems the curvy track is just an optical illusion. From the simulation perspective it's a straight line all the time.
So the question would be only how to create such illusion.

Do you want to copy the visual style of that game, or only the gameplay?

It looks to me that the visual effect of the curvature in that game is generated entirely by shifting scanlines left or right. The sprites are placed on top of that and shifted right or left to match the road. This is not exactly rocket science, but it does involve a fair bit of experimenting to get it right.

If you only want to copy the gameplay, there is an easier option. Just take any off-the-shelves game engine like Unity or Unreal and move an invisible entity along a predefined path in the middle of the road. Then parent the player's car to that entity, but allow it to move along the local x-axis.