Correct. That was the actual constitutional point in issue: could the Congress expand the original jurisdiction of the Supreme Court?
That required the Court to consider whether they had the constitutional jurisdiction to review the constitutionality of an act passed by Congress.
They decided they did have the jurisdiction to review the constitutionality of the Judicature Act, then they reviewed the grant of mandamus in the Act against the list of original jurisdiction of the Supreme Court set out in Article III.
They concluded that Congress could not expand the list of original jurisdiction.
Therefore, the statutory provision for mandamus, giving the Supreme Court the power to order government officials to fulfill legal duties, was unconstitutional.
Since they did not have jurisdiction to order mandamus, the Court dismissed Mr Marbury’s application for mandamus to compel the delivery of his commission.
Without his commission, he never became a federal judge.
Now, there is a difference in that case from the presidential qualifications clause, in that Art. III said that the Court did have jurisdiction to hear such matters under its appellate jurisdiction, once a federal trial court had dealt with it.
But since there is no alternative in the presidential qualifications clause, I think that makes the argument that it can’t be added to all the stronger. There’s nothing else that allows an expansion, unlike the appellate jurisdiction of the Supreme Court, which is in addition to the original jurisdiction.
Text of the jurisdiction clause is here:
Article III, s. 2, clause 2.