Here are some excerpts from Swedenborg's "Arcana Coelestia" that help explain the inner meaning of this chapter:

AC 1651. This chapter treats of the Lord’s temptation combats, which are represented and signified by the wars here described.

AC 1652. The goods and truths in the external man, but which only appeared as goods and truths, were the things from which the Lord fought in His childhood against evils and falsities. The apparent goods and truths are signified by the kings named in (verse 1); but the evils and falsities against which He fought are signified by the kings named in (verse 2); and these were unclean (verse 3).

AC 1653. These evils and falsities against which He fought did not show themselves earlier than in childhood; and then they burst forth, which is signified by their previously serving Chedorlaomer (verse 4).

AC 1654. The Lord then warred against and conquered the persuasions of falsity of all kinds, which are the Rephaim, the Zuzim, the Emim, and the Horites (verses 5, 6); next, the falsities and evils themselves, which are the Amalekite and the Amorite (verse 7) afterwards the other falsities and evils, which are the kings named in (verses 8 to 11).

AC 1655. Apparent truths and goods, which are not in themselves truths and goods, took possession of the external man (verse 12); and the rational man which is "Abram the Hebrew," perceiving this, laid claim to it and liberated it (verses 13 to 16).

AC 1656. After these combats, evil and falsity submitted themselves (verse 17).

AC 1657. The Lord‘s internal man in the interior man, or the Divine in the rational, is Melchizedek, from whom came the benediction after the combats (verses 18 to 20). The tithes are the remains, or the states of good and truth from the combats (verse 20).

AC 1658. The evil and infernal spirits, being overcome, begged for life, and did not care for other things; but nothing was taken from them by the Lord, because He had no strength from their evils and falsities; but they were given into the power (potestas) of good spirits and angels (verses 21-24).

1657. The Lord's Internal Man within the Interior Man, or the Divine within the Rational, is Melchizedek, from whom a blessing came when the conflicts were over, verses 18-20. 'Tenths' is the remnants, or states of good and truth acquired from conflicts, verse 20.