Ah! The same typology is present. Melchizedek was a whisper of Christ–Christ as priest, not according to the Levites, Christ as King, Christ as righteousness, Christ as peace. They should have known. They should have searched the Scriptures so as to not miss their Messiah.
In fact, the Apostle gives another argument for this from tithing. Verse 4 and 5 state that it is the sole privilege of priests to receive tithes. This is by divine command. Abraham gave Melchizedek a tithe, so according to even Abraham Melchizedek was a legitimate priest. Thus, if the Melchizedekian order of priesthood was confirmed by even Abraham, and Christ is of that priesthood, then Christ is confirmed as a priest.