Take another look at the passage:
Raja knew that his roommate Tina had cupcakes hidden in the apartment. He looked everywhere. Including in the clothes hamper, on top of the bookcases, behind the sofa—even under his own bed!—all to no avail.
You chose the second part, He looked everywhere. This part has a main clause: He is the subject; looked is the verb. A fragment will not have a main clause. And remember, fragments don't have to be the shortest part!