here's my short summary:
easterbrook rejects UCC 2-207 because that applies to "battle of the forms," whereas only 1 form was involved here. Instead, he just treats this as a normal contract where the offeror can specify manner of acceptance, and if the offeree complies with that then there is a binding contract. Thus, Gateway specified acceptance-by-opening-the-box, and Hills accepted by opening the box. Thus, there was a contract, and the Hills were bound to its terms.
But in terms of the significance of this case, I think it's important because there are 3 ways you can go about approaching this kind of situation:
1) Use common law/restatement and treat Hill as offeror, Gateway as offeree. Hill offers to buy, Gateway gives a counteroffer by sending the box with new terms, performance is commenced when Hill opens the box, and the last doctrine dictates that Gateway's terms govern. (*note, this would actually only apply to service contracts)
2) Use 2-207 with Hill as offeror, Gateway as offeree. Hill offers to buy, Gateway's new terms are a proposal to contract, but since Hill is a nonmerchant, the terms are only adopted with their consent. Hill did not consent, so even though there was a contract, Hill can recover under this because technically their original terms only governed the contract.
3) Easterbrook's method. Hill is the offeree, and Gateway is the offeror. Gateway specified form of acceptance, Hill performed that specified acceptance, there is a normal contract to which parties are bound.