"In all Cases affecting Ambassadors, other public Ministers and Consuls, and those in which a State shall be Party, the supreme Court shall have original Jurisdiction. In all the other Cases before mentioned, the supreme Court shall have appellate Jurisdiction, both as to Law and Fact..."
If a case was brought to the SCOTUS regarding a person's Constitutional eligibility for office, they would be the deciding authority.
Sorry, but the quoted article doesn't give SCOTUS the power to determine eligibilty, nor does it give it power to remove a sitting president.
Your quote does not say what you believe it does. It is not speaking of the president.