The majority decided to answer a question not part of the case, namely that Congress must act to invoke 14.3. That determination means that the entire amendment is not self-executing. They leaned on the 14.5 for this, though a strict reading would be that the amendment is worded as self-executing with no stipulations and 14.5 only offers Congress an avenue to act for a universal answer to, in this case, the question of the eligibility disability.
The ruling justifies this by saying that it seems nun reasonable for states to have the power of deeming a federal candidate ineligible. That meaning is not stipulated at all in the amendment, and goes in the face of both states' authority to run the election process and states' duty to enforce federal law (in this case the ineligibility of a candidate).
The amendment does not stipulate that the power to enforce sits only with Congress, the bench made this up. The amendment does not limit the authority to enforce the amendment only with the federal government, they made this up. Nowhere in the amendment is it written as non self-executing, to the contrary 14.3 specifically provides a way for Congress to undo the intelligibility after the fact.