And it was this same Melchizedek to whom Abraham paid tithes; yea, even our father Abraham paid tithes of one-tenth part of all he possessed.
Why did Abraham pay his thing to Melchizedek instead of God? Well, Genesis 14:18 says
And Melchizedek king of Salem brought forth bread and wine
so maybe it was more of a tax as he was the King. Or, the same verse also says:
and he was the priest of the most high God.
So maybe he was just the person to collect tithing, like how the Bishop collects our tithing today. The Joseph Smith Translation helps me understand.
And now, Melchizedek was a priest of this order; therefore he obtained peace in Salem, and was called the Prince of peace.
And this Melchizedek, having thus established righteousness, was called the king of heaven by his people, or, in other words, the King of peace.
JST, Genesis 14:33, 36
So Melchizedek was not the King of the land, but it was just a nickname. So my first idea is wrong.
And he lifted up his voice, and he blessed Abram, being the high priest, and the keeper of the storehouse of God;
Him whom God had appointed to receive tithes for the poor.
JST, Genesis 14:37-38
And that verifies my second idea. He is the person who collects the tithing.