The tl;dr is that Theranos makes their own machines, which makes every test that they perform technically a "Lab Developed Test" LDT which doesn't have the same oversight that machines which are sold to others. As long as they make their machines and use their machines, they're effectively exploiting a loophole.

From the article:

The backdrop for this dispute is an unusual regulatory structure that does, in fact, confer upon some–though not all–conventional lab tests an extra layer of validation that Theranos’s do not yet have. Most labs, like Quest and Laboratory Corp. of America, perform many of their routine tests using analyzers they buy from medical-device manufacturers, like Siemens, Olympus, and Beckman Coulter. Before those manufacturers can sell such equipment, they must obtain U.S. Food and Drug Administration approval for the tests those analyzers perform–a process that is in addition to, and more searching than, the audits and proficiency tests required to win CMS certification for the lab itself.

At the same time, for other procedures conventional labs will devise their own lab-developed tests, or LDTs, which they do not have cleared by the FDA. While the FDA takes the position that it could require approval for LDTs, for many years it has said it would forgo that right in the exercise of its “enforcement discretion.”

Theranos, which does not buy any analyzers from third parties, is therefore in a unique position. While it would need FDA approval to sell its own analyzers to other labs, it doesn’t do that. It uses its analyzers only in its own CMS-certified lab. All its tests are therefore LDTs, effectively exempt from FDA oversight.