What made Malkitzedek a Cohen more than Abraham?

Question

1. IIRC, before Mt. Sinai, priestly rights were given to the firstborns.
2. For those who say, Malkitzedek was Shem Ben Noah, he wasn't Noah's firstborn.
3. I don't know if Abraham was a firstborn, but, unlike Malkitzedek, he's openly mentioned to be very special in following God's steps.

What made Malkitzedek a Cohen on a level greater than Abraham to necessitate Abraham's Maaser to him?

Answer 1

The Maharal in Gur Aryeh explains that Noach got bitten by the lion and so he was a Baal mum and unable to be a Kohen. From the three children, Shem was the most worthy so he became the Kohen

ואין ספק שלא היה כהן רק המובחר, וזהו שם, שהרי מקדים אותו הכתוב תחלה "שם חם ויפת" (לעיל י, א), ומאחר שנעשה שם כהן לא ירד מכהונה כל ימי חייו, דאין מורידין בקדושה

Answer 2

In my answer to your similar question I cited R. Saadiah Gaon (Emunot V'Deiot 3:9) who wrote:

The third [problem is presented by] the fact that God commanded all men to offer up sacrifices and then forbade such activities to everyone except Aaron and his children. But this, too, did not constitute an abrogation, for there is not contained in Scripture a single text indicating that all men had been appointed to perform the sacrificial rite. Before the appointment of Aaron it was only who had been appointed to a position similar to his that performed this rite. One who had not been appointed, however, had no right to engage in the performance of the sacrificial rite, neither before nor after the election of Aaron.

(Rosenblatt translation p. 168-19)

If this is true with regard to sacrificial offerings it may well be true with regard to other functions of the priesthood as well.