The concept of privity has to do with legal connections between people or other entities. It is generally the case that a contract cannot be enforced between parties that are not in privity with one another. Parties are in privity if they have some sort of contact or legal connection between them.
In this case, Donald MacPherson bought a car from a retailer. The retailer had bought the car from the Buick Motor Company. The car had been made using various parts, including the wheels made by the wheel company. The question, then, is which of these parties actually had a legal connection to the other.
The only parties that were in privity to one another were the parties that actually bought from or sold to one another. This means that Buick and the wheel company were in privity because Buick bought wheels from the wheel company. It means that Buick and the retailer were in privity because the retailer bought the car from Buick. It means that MacPherson and the retailer were in privity because MacPherson bought from the retailer. But no one else was in privity because no other pair had been party to a purchase. MacPherson, for example, did not buy the car from Buick.
So, the only parties in privity were parties that actually bought from or sold to one another.