The original article confuses OTAs and Aggregators. Expedia and Travelocity are OTAs and have a login to Sabre and other systems as travel agencies. They can book and service your trip. They also use Sabre and others to do the search against the fares and schedules databases, as well as online connectivity to airlines for availability. Kayak, Skyscanner and others are aggregators.
BTW - I led the algorithm design of Sabre's Linux-based search engine about 15 years ago - Travelocity, Expedia and others drove our requirements.