"In 1965, Mr. Martin received a dispensation from all privileges and obligations deriving from his vows as a Jesuit and from priestly ordination."
Fr. Martin was dispensed from priveleges and obligations: as a Jesuit-- (poverty, obedience, papal obedience as a Jesuit, and privileges being salary, shelter, health insurance.
And from priestly ordination: (he was not incardinated in a diocese under a bishop, he was not a member of Opus Dei at his request)
According to his testimony from a 1997 radio interview.
He quoted Paul VI as saying, "Alright, I'll grant you dispensation, do you want me to assign you to a bishop? We've got many who would be glad to have you." He said, "no Holy Father, there is a storm coming over the Church, You yourself have said this. I want to be active in communications and I don't want to be under a bishop that will silence me." Paul VI said, "well, they won't like that. But we'll working something out for you."
He was given by Paul VI a superior in Rome to report to, separate from the Congregational secretaries. He was to give an accounting of his money and this superior was to check on his doctrinal accuracy. He was forbidden to publicly back any political candidate and he was forbidden to personally enter politics.
Yeah, that's the problem, his testimony contradicts the decree (saying Mass happens to be one of the privileges of priestly ordination), and the statement of the Jesuit Vicar General:
I spoke with Fr. Vincent O'Keefe, former vicar general of the Society of Jesus who is now retired. According to Fr. O'Keefe, Malachi Martin was indeed dispensed from his vows of poverty and obedience but not the vow of chastity. At the time Martin requested such dispensation, the Vatican was not dispensing priests who so requested such dispensation from the vow of chastity or celibacy.
Anyone can say that Paul VI said anything to them. That's why his status is unclear.