I don't have any issues running this game natively (without wrappers) on modern hardware. And the game doesn't look anywhere close to your screenshot. Something is very weird.
The "frame jitter" when taking turns seems to be the game problem. The car handling is very unresponsive with the "behind car" camera view. Try switching to bumper camera and you will notice that the car handles much better. It is a problem that even reviewers were complaining about, back when the game was released.
I did, however apply some tweaks to the game.
1. Moved following folders from the disc to the game directory, (because the installer doesn't copy majority of the content onto the drive, so it ends up reading from the disc all the time - causing long load times and other bad stuff):
2. Patched the game to version 242.
3. Used a No-CD "Vitamin" so I don't ruin the disc.
4. Changed the resolution in the .ini and used "Old Games Widescreen Patch" to get the correct aspect ratio.
You can try doing that, maybe that will solve your problem...