challenging contract law question

I don't understand why the person has to be the offeror. It can be the other way round. This is my opinion:

The company of the self-vending machine makes a unilateral offer to the world that whoever pays the stipulated price, he can get a product.

Recall that for unilateral offers, communication of acceptance is not required; merely performing the required act would deem to be an acceptance of the unilateral offer.

Therefore, once the person pays up, there is a valid contract between him and the company of the self vending machine.

In this case, the person is the offeree, as he accepted the "offer to sell".
The company of the self vending machine is the offeror as it unilaterally offers to sell its product.

I don't agree with your analysis that the person is the offeror. If you argue the he made an offer to buy to the company of the vending machine by inserting the coins, you can hardly identify when the company has accepted the offer.

(a) In my version, the company of the self vending machine is clearly the offeror, or in your view, the offeree.

(b) In my version, the company of the self vending machine is also clearly the offeror, or in your view, the offeree. This is because there is no privity of contract between the company of the product and the person. The company of the self vending machine made an offer to sell, and it was accepted by the person by paying for the products. The contract is clearly between the company of the self vending machine and the person.

Read Donoghue v Stevenson. In this landmark tort case, the plaintiff fell sick after drinking a beverage with a snail in it. The plaintiff could only sue the producer of the beverage through tort since there is no privity of contract between them.