Tiny flakes of plastic, generated by the wear and tear of normal driving, eventually accumulate in the soil, in rivers and lakes, and even in our food.
A plastic is just a material made from polymers, you are the one adding artificial limitations on what polymers can be used.
The belts in tires use both nylon and polyester which are both plastics by anyone’s definition. So even by your strict definition, tires are made up, at least in part, by plastic.
Synthetic rubber is not plastic. It is from petrochemicals but not the same chemical substance.
A plastic is just a material made from polymers, you are the one adding artificial limitations on what polymers can be used. The belts in tires use both nylon and polyester which are both plastics by anyone’s definition. So even by your strict definition, tires are made up, at least in part, by plastic.