That's not comparable. Netflix did not have a monopoly on "shipping DVDs". Plenty of retailers, online or brick-and-mortar, did that at the same time Netflix did, and video rental places were still going. Some of which would deliver movies (the local Marcos near me had a deal with a local Family Video where if you bought a large pizza they would bring you both the pizza and a movie of your choice from Family Video, assuming it was in stock).
It's not that they have a search engine. It's what they're doing to advertisers, websight owners, and consumers with it that is the problem. It's them abusing their market position to the detriment of customers and competitors.
Nor has Netflix had a monopoly on streaming.